bibliography.bib

@Article{eLISA-I,
  author           = {Antoine Klein and Enrico Barausse and Alberto Sesana and Antoine Petiteau and Emanuele Berti and Stanislav Babak and Jonathan Gair and Sofiane Aoudia and Ian Hinder and Frank Ohme and Barry Wardell},
  journal          = {Phys. Rev. D 93, 024003 (2016)},
  title            = {Science with the space-based interferometer eLISA. I: Supermassive black hole binaries},
  year             = {2015},
  month            = nov,
  abstract         = {We compare the science capabilities of different eLISA mission designs, including four-link (two-arm) and six-link (three-arm) configurations with different arm lengths, low-frequency noise sensitivities and mission durations. For each of these configurations we consider a few representative massive black hole formation scenarios. These scenarios are chosen to explore two physical mechanisms that greatly affect eLISA rates, namely (i) black hole seeding, and (ii) the delays between the merger of two galaxies and the merger of the black holes hosted by those galaxies. We assess the eLISA parameter estimation accuracy using a Fisher matrix analysis with spin-precessing, inspiral-only waveforms. We quantify the information present in the merger and ringdown by rescaling the inspiral-only Fisher matrix estimates using the signal-to-noise ratio from non-precessing inspiral-merger-ringdown phenomenological waveforms, and from a reduced set of precessing numerical relativity/post-Newtonian hybrid waveforms. We find that all of the eLISA configurations considered in our study should detect some massive black hole binaries. However, configurations with six links and better low-frequency noise will provide much more information on the origin of black holes at high redshifts and on their accretion history, and they may allow the identification of electromagnetic counterparts to massive black hole mergers.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:17:03},
  doi              = {10.1103/PhysRevD.93.024003},
  eprint           = {1511.05581},
  file             = {:eLISA-I.pdf:PDF},
  keywords         = {gr-qc, astro-ph.HE},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {gr-qc},
  priority         = {prio3},
}

@Article{GW170817,
  author           = {The LIGO Scientific Collaboration and The Virgo Collaboration},
  journal          = {Phys. Rev. Lett. 119 161101 (2017)},
  title            = {GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral},
  year             = {2017},
  month            = oct,
  abstract         = {On August 17, 2017 at 12:41:04 UTC the Advanced LIGO and Advanced Virgo gravitational-wave detectors made their first observation of a binary neutron star inspiral. The signal, GW170817, was detected with a combined signal-to-noise ratio of 32.4 and a false-alarm-rate estimate of less than one per $8.0\times10^4$ years. We infer the component masses of the binary to be between 0.86 and 2.26 $M_\odot$, in agreement with masses of known neutron stars. Restricting the component spins to the range inferred in binary neutron stars, we find the component masses to be in the range 1.17 to 1.60 $M_\odot$, with the total mass of the system $2.74^{+0.04}_{-0.01}\,M_\odot$. The source was localized within a sky region of 28 deg$^2$ (90\% probability) and had a luminosity distance of $40^{+8}_{-14}$ Mpc, the closest and most precisely localized gravitational-wave signal yet. The association with the gamma-ray burst GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short gamma-ray bursts. Subsequent identification of transient counterparts across the electromagnetic spectrum in the same location further supports the interpretation of this event as a neutron star merger. This unprecedented joint gravitational and electromagnetic observation provides insight into astrophysics, dense matter, gravitation and cosmology.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:18:29},
  doi              = {10.1103/PhysRevLett.119.161101},
  eprint           = {1710.05832},
  file             = {:GW170817.pdf:PDF},
  groups           = {Observations},
  keywords         = {gr-qc, astro-ph.HE},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {gr-qc},
}

@Article{Chen2017,
  author           = {Hsin-Yu Chen and Maya Fishbach and Daniel E. Holz},
  title            = {A 2 per cent Hubble constant measurement from standard sirens within 5 years},
  year             = {2017},
  month            = dec,
  abstract         = {Gravitational wave coalescence events provide an entirely new way to determine the Hubble constant, with the absolute distance calibration provided by the theory of general relativity. This standard siren method was utilized to measure the Hubble constant using LIGO-Virgo's detection of the binary neutron-star merger GW170817, as well as optical identifications of the host galaxy, NGC 4993. The novel and independent measurement is of particular interest given the existing tension between the value of the Hubble constant determined using Type Ia supernovae via the local distance ladder ($73.24 \pm 1.74$) and that from Cosmic Microwave Background observations ($66.93 \pm 0.62$) by $\sim 3$ sigma. Local distance ladder observations may achieve a precision of $1\%$ within 5 years, but at present there are no indications that further observations will substantially reduce the existing discrepancies. In addition to clarifying the discrepancy between existing low and high-redshift measurements, a precision measurement of the Hubble constant is of crucial value in elucidating the nature of the dark energy. Here we show that LIGO and Virgo can be expected to constrain the Hubble constant to a precision of $\sim2\%$ within 5 years and $\sim1\%$ within a decade.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:18:58},
  doi              = {10.1038/s41586-018-0606-0},
  eprint           = {1712.06531},
  file             = {:Chen2017.pdf:PDF},
  keywords         = {astro-ph.CO, astro-ph.HE},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {astro-ph.CO},
  ranking          = {rank1},
}

@Article{eLISA-II,
  author           = {Chiara Caprini and Mark Hindmarsh and Stephan Huber and Thomas Konstandin and Jonathan Kozaczuk and Germano Nardini and Jose Miguel No and Antoine Petiteau and Pedro Schwaller and Geraldine Servant and David J. Weir},
  title            = {Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions},
  year             = {2015},
  month            = dec,
  abstract         = {We investigate the potential for the eLISA space-based interferometer to detect the stochastic gravitational wave background produced by strong first-order cosmological phase transitions. We discuss the resulting contributions from bubble collisions, magnetohydrodynamic turbulence, and sound waves to the stochastic background, and estimate the total corresponding signal predicted in gravitational waves. The projected sensitivity of eLISA to cosmological phase transitions is computed in a model-independent way for various detector designs and configurations. By applying these results to several specific models, we demonstrate that eLISA is able to probe many well-motivated scenarios beyond the Standard Model of particle physics predicting strong first-order cosmological phase transitions in the early Universe.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:19:18},
  doi              = {10.1088/1475-7516/2016/04/001},
  eprint           = {1512.06239},
  file             = {:eLISA-II.pdf:PDF},
  keywords         = {astro-ph.CO, gr-qc, hep-ph},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
}

@Article{Caprini2016,
  author           = {Chiara Caprini and Nicola Tamanini},
  journal          = {Journal of Cosmology and Astroparticle Physics},
  title            = {Constraining early and interacting dark energy with gravitational wave standard sirens: the potential of the {eLISA} mission},
  year             = {2016},
  month            = {oct},
  number           = {10},
  pages            = {006--006},
  volume           = {2016},
  abstract         = {We perform a forecast analysis of the capability of the eLISA space-based interferometer to constrain models of early and interacting dark energy using gravitational wave standard sirens. We employ simulated catalogues of standard sirens given by merging massive black hole binaries visible by eLISA, with an electromagnetic counterpart detectable by future telescopes. We consider three-arms mission designs with arm length of 1, 2 and 5 million km, 5 years of mission duration and the best-level low frequency noise as recently tested by the LISA Pathfinder. Standard sirens with eLISA give access to an intermediate range of redshift $1\lesssim z \lesssim 8$, and can therefore provide competitive constraints on models where the onset of the deviation from $\Lambda$CDM (i.e. the epoch when early dark energy starts to be non-negligible, or when the interaction with dark matter begins) occurs relatively late, at $z\lesssim 6$. If instead early or interacting dark energy is relevant already in the pre-recombination era, current cosmological probes (especially the cosmic microwave background) are more efficient than eLISA in constraining these models, except possibly in the interacting dark energy model if the energy exchange is proportional to the energy density of dark energy.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:19:43},
  doi              = {10.1088/1475-7516/2016/10/006},
  eprint           = {1607.08755},
  file             = {:Caprini2016.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {astro-ph.CO, gr-qc},
  modificationdate = {2022-03-22T14:09:39},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
  publisher        = {{IOP} Publishing},
}

@Article{emcee,
  author           = {Daniel Foreman-Mackey and David W. Hogg and Dustin Lang and Jonathan Goodman},
  title            = {emcee: The MCMC Hammer},
  year             = {2012},
  month            = feb,
  abstract         = {We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to $\sim N^2$ for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation and API. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the MIT License.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:20:14},
  doi              = {10.1086/670067},
  eprint           = {1202.3665},
  file             = {:emcee.pdf:PDF},
  groups           = {Software},
  keywords         = {astro-ph.IM, physics.comp-ph, stat.CO},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {astro-ph.IM},
}

@Article{Belgacem2018,
  author           = {Enis Belgacem and Yves Dirian and Stefano Foffa and Michele Maggiore},
  journal          = {Physical Review D},
  title            = {Modified gravitational-wave propagation and standard sirens},
  year             = {2018},
  month            = {jul},
  number           = {2},
  pages            = {023510},
  volume           = {98},
  abstract         = {Studies of dark energy at advanced gravitational-wave (GW) interferometers normally focus on the dark energy equation of state $w_{\rm DE}(z)$. However, modified gravity theories that predict a non-trivial dark energy equation of state generically also predict deviations from general relativity in the propagation of GWs across cosmological distances, even in theories where the speed of gravity is equal to $c$. We find that, in generic modified gravity models, the effect of modified GW propagation dominates over that of $w_{\rm DE}(z)$, making modified GW propagation a crucial observable for dark energy studies with standard sirens. We present a convenient parametrization of the effect in terms of two parameters $(\Xi_0,n)$, analogue to the $(w_0,w_a)$ parametrization of the dark energy equation of state, and we give a limit from the LIGO/Virgo measurement of $H_0$ with the neutron star binary GW170817. We then perform a Markov Chain Monte Carlo analysis to estimate the sensitivity of the Einstein Telescope (ET) to the cosmological parameters, including $(\Xi_0,n)$, both using only standard sirens, and combining them with other cosmological datasets. In particular, the Hubble parameter can be measured with an accuracy better than $1\%$ already using only standard sirens while, when combining ET with current CMB+BAO+SNe data, $\Xi_0$ can be measured to $0.8\%$ . We discuss the predictions for modified GW propagation of a specific nonlocal modification of gravity, recently developed by our group, and we show that they are within the reach of ET. Modified GW propagation also affects the GW transfer function, and therefore the tensor contribution to the ISW effect.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:20:45},
  doi              = {10.1103/physrevd.98.023510},
  eprint           = {1805.08731},
  file             = {:Belgacem2018.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {gr-qc, astro-ph.CO, hep-th},
  modificationdate = {2022-03-21T22:00:36},
  primaryclass     = {gr-qc},
  priority         = {prio3},
  publisher        = {American Physical Society ({APS})},
}

@Article{Belgacem2017,
  author           = {Enis Belgacem and Yves Dirian and Stefano Foffa and Michele Maggiore},
  title            = {Nonlocal gravity. Conceptual aspects and cosmological predictions},
  year             = {2017},
  month            = dec,
  abstract         = {Even if the fundamental action of gravity is local, the corresponding quantum effective action, that includes the effect of quantum fluctuations, is a nonlocal object. These nonlocalities are well understood in the ultraviolet regime but much less in the infrared, where they could in principle give rise to important cosmological effects. Here we systematize and extend previous work of our group, in which it is assumed that a mass scale $\Lambda$ is dynamically generated in the infrared, giving rise to nonlocal terms in the quantum effective action of gravity. We give a detailed discussion of conceptual aspects related to nonlocal gravity and of the cosmological consequences of these models. The requirement of providing a viable cosmological evolution severely restricts the form of the nonlocal terms, and selects a model (the so-called RR model) that corresponds to a dynamical mass generation for the conformal mode. For such a model: (1) there is a FRW background evolution, where the nonlocal term acts as an effective dark energy with a phantom equation of state, providing accelerated expansion without a cosmological constant. (2) Cosmological perturbations are well behaved. (3) Implementing the model in a Boltzmann code and comparing with observations we find that the RR model fits the CMB, BAO, SNe, structure formation data and local $H_0$ measurements at a level statistically equivalent to $\Lambda$CDM. (4) Bayesian parameter estimation shows that the value of $H_0$ obtained in the RR model is higher than in $\Lambda$CDM, reducing to $2.0\sigma$ the tension with the value from local measurements. (5) The RR model provides a prediction for the sum of neutrino masses that falls within the limits set by oscillation and terrestrial experiments. (6) Gravitational waves propagate at the speed of light, complying with the limit from GW170817/GRB 170817A.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:22:30},
  doi              = {10.1088/1475-7516/2018/03/002},
  eprint           = {1712.07066},
  file             = {:Belgacem2017.pdf:PDF},
  keywords         = {hep-th, astro-ph.CO, gr-qc},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {hep-th},
}

@Article{Fonseca2021,
  author           = {Vitor da Fonseca and Tiago Barreiro and Nelson J. Nunes},
  journal          = {Physics of the Dark Universe, Volume 35, 2022, 100940},
  title            = {A simple parametrisation for coupled dark energy},
  year             = {2021},
  month            = apr,
  abstract         = {As an alternative to the popular parametrisations of the dark energy equation of state, we construct a quintessence model where the scalar field has a linear dependence on the number of e-folds. Constraints on more complex models are typically limited by the degeneracies that increase with the number of parameters. The proposed parametrisation conveniently constrains the evolution of the dark energy equation of state as it allows for a wide variety of time evolutions. We also consider a non-minimal coupling to cold dark matter. We fit the model with Planck and KiDS observational data. The CMB favours a non-vanishing coupling with energy transfer from dark energy to dark matter. Conversely, gravitational weak lensing measurements slightly favour energy transfer from dark matter to dark energy, with a substantial departure of the dark energy equation of state from -1.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:23:02},
  doi              = {10.1016/j.dark.2021.100940},
  eprint           = {2104.14889},
  file             = {:Fonseca2021.pdf:PDF},
  keywords         = {astro-ph.CO, gr-qc},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {astro-ph.CO},
}

@Article{Baker2021,
  author           = {Tessa Baker and Ian Harrison},
  journal          = {Journal of Cosmology and Astroparticle Physics},
  title            = {Constraining Scalar-Tensor Modified Gravity with Gravitational Waves and Large Scale Structure Surveys},
  year             = {2021},
  month            = {jan},
  number           = {01},
  pages            = {068--068},
  volume           = {2021},
  abstract         = {The first multi-messenger gravitational wave event has had a transformative effect on the space of modified gravity models. In this paper we study the enhanced tests of gravity that are possible with a future set of gravitational wave standard siren events. We perform MCMC constraint forecasts for parameters in Horndeski scalar-tensor theories. In particular, we focus on the complementarity of gravitational waves with electromagnetic large-scale structure data from galaxy surveys. We find that the addition of fifty low redshift ($z \lesssim 0.2$) standard sirens from the advanced LIGO network offers only a modest improvement (a factor 1.1 -- 1.3, where 1.0 is no improvement) over existing constraints from electromagnetic observations of large-scale structures. In contrast, high redshift (up to $z \sim 10$) standard sirens from the future LISA satellite will improve constraints on the time evolution of the Planck mass in Horndeski theories by a factor $\sim 5$. By simulating different scenarios, we find this improvement to be robust to marginalisation over unknown merger inclination angles and to variation between three plausible models for the merger source population.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:23:20},
  doi              = {10.1088/1475-7516/2021/01/068},
  eprint           = {2007.13791},
  file             = {:Baker2020.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {astro-ph.CO, gr-qc},
  modificationdate = {2022-03-22T14:08:21},
  primaryclass     = {astro-ph.CO},
  publisher        = {{IOP} Publishing},
}

@Article{LCDM-R2021,
  author           = {Leandros Perivolaropoulos and Foteini Skara},
  title            = {Challenges for $\Lambda$CDM: An update},
  year             = {2021},
  month            = may,
  abstract         = {A number of challenges of the standard $\Lambda$CDM model has been emerging during the past few years as the accuracy of cosmological observations improves. In this review we discuss in a unified manner many existing signals in cosmological and astrophysical data that appear to be in some tension ($2\sigma$ or larger) with the standard $\Lambda$CDM model as defined by the Planck18 parameter values. In addition to the major well studied $5\sigma$ challenge of $\Lambda$CDM (the Hubble $H_0$ crisis) and other well known tensions (the growth tension and the lensing amplitude $A_L$ anomaly), we discuss a wide range of other less discussed less-standard signals which appear at a lower statistical significance level than the $H_0$ tension (also known as 'curiosities' in the data) which may also constitute hints towards new physics. For example such signals include cosmic dipoles (the fine structure constant $\alpha$, velocity and quasar dipoles), CMB asymmetries, BAO Ly$\alpha$ tension, age of the Universe issues, the Lithium problem, small scale curiosities like the core-cusp and missing satellite problems, quasars Hubble diagram, oscillating short range gravity signals etc. The goal of this pedagogical review is to collectively present the current status of these signals and their level of significance, with emphasis to the Hubble crisis and refer to recent resources where more details can be found for each signal. We also briefly discuss possible theoretical approaches that can potentially explain the non-standard nature of some of these signals.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:24:16},
  eprint           = {2105.05208},
  file             = {:LCDM-R2021.pdf:PDF},
  groups           = {Review},
  keywords         = {astro-ph.CO, gr-qc, hep-ph, hep-th},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
}

@Article{Tamanini2017,
  author           = {Nicola Tamanini},
  journal          = {Journal of Physics: Conference Series},
  title            = {Late time cosmology with {LISA}: Probing the cosmic expansion with massive black hole binary mergers as standard sirens},
  year             = {2017},
  month            = {may},
  pages            = {012029},
  volume           = {840},
  abstract         = {This paper summarises the potential of the LISA mission to constrain the expansion history of the universe using massive black hole binary mergers as gravitational wave standard sirens. After briefly reviewing the concept of standard siren, the analysis and methodologies of Ref. [1] are briefly outlined to show how LISA can be used as a cosmological probe, while a selection of results taken from Refs. [1,2] is presented in order to estimate the power of LISA in constraining cosmological parameters.},
  archiveprefix    = {arXiv},
  doi              = {10.1088/1742-6596/840/1/012029},
  eprint           = {1612.02634},
  file             = {:Tamanini2016.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {astro-ph.CO},
  modificationdate = {2022-03-21T21:55:29},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
  publisher        = {{IOP} Publishing},
}

@Article{ELISA-III,
  author           = {Nicola Tamanini and Chiara Caprini and Enrico Barausse and Alberto Sesana and Antoine Klein and Antoine Petiteau},
  journal          = {JCAP 1604 (2016) no.04, 002},
  title            = {Science with the space-based interferometer eLISA. III: Probing the expansion of the Universe using gravitational wave standard sirens},
  year             = {2016},
  month            = jan,
  abstract         = {We investigate the capability of various configurations of the space interferometer eLISA to probe the late-time background expansion of the universe using gravitational wave standard sirens. We simulate catalogues of standard sirens composed by massive black hole binaries whose gravitational radiation is detectable by eLISA, and which are likely to produce an electromagnetic counterpart observable by future surveys. The main issue for the identification of a counterpart resides in the capability of obtaining an accurate enough sky localisation with eLISA. This seriously challenges the capability of four-link (2 arm) configurations to successfully constrain the cosmological parameters. Conversely, six-link (3 arm) configurations have the potential to provide a test of the expansion of the universe up to $z\sim 8$ which is complementary to other cosmological probes based on electromagnetic observations only. In particular, in the most favourable scenarios, they can provide a significant constraint on $H_0$ at the level of 0.5\%. Furthermore, $(\Omega_M, \Omega_\Lambda)$ can be constrained to a level competitive with present SNIa results. On the other hand, the lack of massive black hole binary standard sirens at low redshift allows to constrain dark energy only at the level of few percent.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:25:34},
  doi              = {10.1088/1475-7516/2016/04/002},
  eprint           = {1601.07112},
  file             = {:ELISA-III.pdf:PDF},
  keywords         = {astro-ph.CO, astro-ph.HE, gr-qc},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
}

@Article{Maggiore2020,
  author           = {Michele Maggiore and Chris Van Den Broeck and Nicola Bartolo and Enis Belgacem and Daniele Bertacca and Marie Anne Bizouard and Marica Branchesi and Sebastien Clesse and Stefano Foffa and Juan Garc{\'{\i}}a-Bellido and Stefan Grimm and Jan Harms and Tanja Hinderer and Sabino Matarrese and Cristiano Palomba and Marco Peloso and Angelo Ricciardone and Mairi Sakellariadou},
  journal          = {Journal of Cosmology and Astroparticle Physics},
  title            = {Science case for the Einstein telescope},
  year             = {2020},
  month            = {mar},
  number           = {03},
  pages            = {050--050},
  volume           = {2020},
  abstract         = {The Einstein Telescope (ET), a proposed European ground-based gravitational-wave detector of third-generation, is an evolution of second-generation detectors such as Advanced LIGO, Advanced Virgo, and KAGRA which could be operating in the mid 2030s. ET will explore the universe with gravitational waves up to cosmological distances. We discuss its main scientific objectives and its potential for discoveries in astrophysics, cosmology and fundamental physics.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:27:33},
  doi              = {10.1088/1475-7516/2020/03/050},
  eprint           = {1912.02622},
  file             = {:Maggiore2019.pdf:PDF},
  keywords         = {astro-ph.CO, astro-ph.HE, gr-qc},
  modificationdate = {2022-03-21T22:08:51},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
  publisher        = {{IOP} Publishing},
}

@Article{Speri2021,
  author           = {Lorenzo Speri and Nicola Tamanini and Robert R. Caldwell and Jonathan R. Gair and Benjamin Wang},
  journal          = {Physical Review D},
  title            = {Testing the quasar Hubble diagram with {LISA} standard sirens},
  year             = {2021},
  month            = {apr},
  number           = {8},
  pages            = {083526},
  volume           = {103},
  abstract         = {Quasars have recently been used as an absolute distance indicator, extending the Hubble diagram to high redshift to reveal a deviation from the expansion history predicted for the standard, $\Lambda$CDM cosmology. Here we show that the Laser Interferometer Space Antenna (LISA) will efficiently test this claim with standard sirens at high redshift, defined by the coincident gravitational wave (GW) and electromagnetic (EM) observations of the merger of massive black hole binaries (MBHBs). Assuming a fiducial $\Lambda$CDM cosmology for generating mock standard siren datasets, the evidence for the $\Lambda$CDM model with respect to an alternative model inferred from quasar data is investigated. By simulating many realizations of possible future LISA observations, we find that for $50\%$ of these realizations (median result) 4 MBHB standard siren measurements will suffice to strongly differentiate between the two models, while 14 standard sirens will yield a similar result in $95\%$ of the realizations. In addition, we investigate the measurement precision of cosmological parameters as a function of the number of observed LISA MBHB standard sirens, finding that 15 events will on average achieve a relative precision of 5\% for $H_0$, reducing to 3\% and 2\% with 25 and 40 events, respectively. Our investigation clearly highlights the potential of LISA as a cosmological probe able to accurately map the expansion of the universe at $z\gtrsim 2$, and as a tool to cross-check and cross-validate cosmological EM measurements with complementary GW observations.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:28:55},
  doi              = {10.1103/physrevd.103.083526},
  eprint           = {2010.09049},
  file             = {:Speri2020.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {astro-ph.CO, gr-qc},
  modificationdate = {2022-03-21T22:15:56},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
  publisher        = {American Physical Society ({APS})},
}

@Article{LISA-proposal,
  author           = {Pau Amaro-Seoane and Heather Audley and Stanislav Babak and John Baker and Enrico Barausse and Peter Bender and Emanuele Berti and Pierre Binetruy and Michael Born and Daniele Bortoluzzi and Jordan Camp and Chiara Caprini and Vitor Cardoso and Monica Colpi and John Conklin and Neil Cornish and Curt Cutler and Karsten Danzmann and Rita Dolesi and Luigi Ferraioli and Valerio Ferroni and Ewan Fitzsimons and Jonathan Gair and Lluis Gesa Bote and Domenico Giardini and Ferran Gibert and Catia Grimani and Hubert Halloin and Gerhard Heinzel and Thomas Hertog and Martin Hewitson and Kelly Holley-Bockelmann and Daniel Hollington and Mauro Hueller and Henri Inchauspe and Philippe Jetzer and Nikos Karnesis and Christian Killow and Antoine Klein and Bill Klipstein and Natalia Korsakova and Shane L Larson and Jeffrey Livas and Ivan Lloro and Nary Man and Davor Mance and Joseph Martino and Ignacio Mateos and Kirk McKenzie and Sean T McWilliams and Cole Miller and Guido Mueller and Germano Nardini and Gijs Nelemans and Miquel Nofrarias and Antoine Petiteau and Paolo Pivato and Eric Plagnol and Ed Porter and Jens Reiche and David Robertson and Norna Robertson and Elena Rossi and Giuliana Russano and Bernard Schutz and Alberto Sesana and David Shoemaker and Jacob Slutsky and Carlos F. Sopuerta and Tim Sumner and Nicola Tamanini and Ira Thorpe and Michael Troebs and Michele Vallisneri and Alberto Vecchio and Daniele Vetrugno and Stefano Vitale and Marta Volonteri and Gudrun Wanner and Harry Ward and Peter Wass and William Weber and John Ziemer and Peter Zweifel},
  title            = {Laser Interferometer Space Antenna},
  year             = {2017},
  month            = feb,
  abstract         = {Following the selection of The Gravitational Universe by ESA, and the successful flight of LISA Pathfinder, the LISA Consortium now proposes a 4 year mission in response to ESA's call for missions for L3. The observatory will be based on three arms with six active laser links, between three identical spacecraft in a triangular formation separated by 2.5 million km. LISA is an all-sky monitor and will offer a wide view of a dynamic cosmos using Gravitational Waves as new and unique messengers to unveil The Gravitational Universe. It provides the closest ever view of the infant Universe at TeV energy scales, has known sources in the form of verification binaries in the Milky Way, and can probe the entire Universe, from its smallest scales near the horizons of black holes, all the way to cosmological scales. The LISA mission will scan the entire sky as it follows behind the Earth in its orbit, obtaining both polarisations of the Gravitational Waves simultaneously, and will measure source parameters with astrophysically relevant sensitivity in a band from below $10^{-4}\,$Hz to above $10^{-1}\,$Hz.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:29:21},
  eprint           = {1702.00786},
  file             = {:LISA-proposal.pdf:PDF},
  keywords         = {astro-ph.IM},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {astro-ph.IM},
  priority         = {prio3},
}

@Article{Corman2021,
  author           = {Maxence Corman and Abhirup Ghosh and Celia Escamilla-Rivera and Martin A. Hendry and Sylvain Marsat and Nicola Tamanini},
  title            = {Constraining cosmological extra dimensions with gravitational wave standard sirens: from theory to current and future multi-messenger observations},
  year             = {2021},
  month            = sep,
  abstract         = {The propagation of gravitational waves (GWs) at cosmological distances offers a new way to test the gravitational interaction at the largest scales. Many modified theories of gravity, usually introduced to explain the observed acceleration of the universe, can be probed in an alternative and complementary manner with respect to standard electromagnetic (EM) observations. In this paper we consider a homogeneous and isotropic cosmology with extra spatial dimensions at large scales, which represents a simple phenomenological prototype for extra-dimensional modified gravity cosmological models. By assuming that gravity propagates through the higher-dimensional spacetime, while photons are constrained to the usual four dimensions of general relativity, we derive from first principles the relation between the luminosity distance measured by GW detectors and the one inferred by EM observations. We then use this relation to constrain the number of cosmological extra dimensions with the binary neutron star event GW170817 and the binary black hole merger GW190521. We further provide forecasts for the Laser Interferometer Space Antenna (LISA) by simulating multi-messenger observations of massive black hole binary (MBHB) mergers. This paper extends and updates previous analyses which crucially neglected an additional redshift dependency in the GW-EM luminosity distance relation which affects results obtained from multi-messenger GW events at high redshift, in particular constraints expected from LISA MBHBs.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:29:56},
  eprint           = {2109.08748},
  file             = {:Corman2021.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {gr-qc, astro-ph.CO},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {gr-qc},
  priority         = {prio3},
}

@Article{Belgacem2019,
  author           = {Enis Belgacem and Gianluca Calcagni and Marco Crisostomi and Charles Dalang and Yves Dirian and Jose Mar{\'{\i}}a Ezquiaga and Matteo Fasiello and Stefano Foffa and Alexander Ganz and Juan Garc{\'{\i}}a-Bellido and Lucas Lombriser and Michele Maggiore and Nicola Tamanini and Gianmassimo Tasinato and Miguel Zumalac{\'{a}}rregui and Enrico Barausse and Nicola Bartolo and Daniele Bertacca and Antoine Klein and Sabino Matarrese and Mairi Sakellariadou},
  journal          = {Journal of Cosmology and Astroparticle Physics},
  title            = {Testing modified gravity at cosmological distances with {LISA} standard sirens},
  year             = {2019},
  month            = {jul},
  number           = {07},
  pages            = {024--024},
  volume           = {2019},
  abstract         = {Modifications of General Relativity leave their imprint both on the cosmic expansion history through a non-trivial dark energy equation of state, and on the evolution of cosmological perturbations in the scalar and in the tensor sectors. In particular, the modification in the tensor sector gives rise to a notion of gravitational-wave (GW) luminosity distance, different from the standard electromagnetic luminosity distance, that can be studied with standard sirens at GW detectors such as LISA or third-generation ground based experiments. We discuss the predictions for modified GW propagation from some of the best studied theories of modified gravity, such as Horndeski or the more general degenerate higher order scalar-tensor (DHOST) theories, non-local infrared modifications of gravity, bigravity theories and the corresponding phenomenon of GW oscillation, as well as theories with extra or varying dimensions. We show that modified GW propagation is a completely generic phenomenon in modified gravity. We then use a simple parametrization of the effect in terms of two parameters $(\Xi_0,n)$, that is shown to fit well the results from a large class of models, to study the prospects of observing modified GW propagation using supermassive black hole binaries as standard sirens with LISA. We construct mock source catalogs and perform detailed Markov Chain Monte Carlo studies of the likelihood obtained from LISA standard sirens alone, as well as by combining them with CMB, BAO and SNe data to reduce the degeneracies between cosmological parameters. We find that the combination of LISA with the other cosmological datasets allows one to measure the parameter $\Xi_0$ that characterizes modified GW propagation to the percent level accuracy, sufficient to test several modified gravity theories. [Abridged]},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:30:31},
  doi              = {10.1088/1475-7516/2019/07/024},
  eprint           = {1906.01593},
  file             = {:Belgacem2019.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {astro-ph.CO, gr-qc, hep-th},
  modificationdate = {2022-03-21T22:23:44},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
  publisher        = {{IOP} Publishing},
}

@Article{GW190521,
  author           = {The LIGO Scientific Collaboration and the Virgo Collaboration},
  journal          = {Astrophys. J. Lett. 900, L13 (2020)},
  title            = {Properties and astrophysical implications of the 150 Msun binary black hole merger GW190521},
  year             = {2020},
  month            = sep,
  abstract         = {The gravitational-wave signal GW190521 is consistent with a binary black hole merger source at redshift 0.8 with unusually high component masses, $85^{+21}_{-14}\,M_{\odot}$ and $66^{+17}_{-18}\,M_{\odot}$, compared to previously reported events, and shows mild evidence for spin-induced orbital precession. The primary falls in the mass gap predicted by (pulsational) pair-instability supernova theory, in the approximate range $65 - 120\,M_{\odot}$. The probability that at least one of the black holes in GW190521 is in that range is 99.0\%. The final mass of the merger $(142^{+28}_{-16}\,M_{\odot})$ classifies it as an intermediate-mass black hole. Under the assumption of a quasi-circular binary black hole coalescence, we detail the physical properties of GW190521's source binary and its post-merger remnant, including component masses and spin vectors. Three different waveform models, as well as direct comparison to numerical solutions of general relativity, yield consistent estimates of these properties. Tests of strong-field general relativity targeting the merger-ringdown stages of coalescence indicate consistency of the observed signal with theoretical predictions. We estimate the merger rate of similar systems to be $0.13^{+0.30}_{-0.11}\,{\rm Gpc}^{-3}\,\rm{yr}^{-1}$. We discuss the astrophysical implications of GW190521 for stellar collapse, and for the possible formation of black holes in the pair-instability mass gap through various channels: via (multiple) stellar coalescence, or via hierarchical merger of lower-mass black holes in star clusters or in active galactic nuclei. We find it to be unlikely that GW190521 is a strongly lensed signal of a lower-mass black hole binary merger. We also discuss more exotic possible sources for GW190521, including a highly eccentric black hole binary, or a primordial black hole binary.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:30:56},
  doi              = {10.3847/2041-8213/aba493},
  eprint           = {2009.01190},
  file             = {:GW190521.pdf:PDF},
  groups           = {Observations},
  keywords         = {astro-ph.HE, gr-qc},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {astro-ph.HE},
}

@Article{Lagos2019,
  author           = {Macarena Lagos and Maya Fishbach and Philippe Landry and Daniel E. Holz},
  journal          = {Phys. Rev. D 99, 083504 (2019)},
  title            = {Standard sirens with a running Planck mass},
  year             = {2019},
  month            = jan,
  abstract         = {We consider the effect of a time-varying Planck mass on the propagation of gravitational waves (GWs). A running Planck mass arises naturally in several modified gravity theories, and here we focus on those that carry an additional dark energy field responsible for the late-time accelerated expansion of the universe, yet--like general relativity (GR)--propagate only two GW polarizations, both traveling at the speed of light. Because a time-varying Planck mass affects the amplitude of the GWs and therefore the inferred distance to the source, standard siren measurements of $H_0$ are degenerate with the parameter $c_M$ characterizing the time-varying Planck mass, where $c_M=0$ corresponds to GR with a constant Planck mass. The effect of non-zero $c_M$ will have a noticeable impact on GWs emitted by binary neutron stars (BNSs) at the sensitivities and distances observable by ground-based GW detectors such as advanced LIGO and A+, implying that standard siren measurements can provide joint constraints on $H_0$ and $c_M$. Assuming a $\Lambda$CDM evolution of the universe and taking Planck's measurement of $H_0$ as a prior, we find that GW170817 constrains $c_M = -9^{+21}_{-28}$ ($68.3\%$ credibility). We also discuss forecasts, finding that if we assume $H_0$ is known independently, then 100 BNS events detected by advanced LIGO can constrain $c_M$ to within $\pm0.9$. This is comparable to the current best constraints from cosmology. Similarly, for 100 LIGO A+ BNS detections, it is possible to constrain $c_M$ to $\pm0.5$. When analyzing joint $H_0$ and $c_M$ constraints we find that $\sim 400$ LIGO A+ events are needed to constrain $H_0$ to $1\%$ accuracy. Finally, we discuss the possibility of a nonzero value of $c_M$ biasing standard siren $H_0$ measurements from 100 LIGO A+ detections, and find that $c_M=+1.35$ could bias $H_0$ by 3-4$\sigma$ too low if we incorrectly assume $c_M=0$.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:31:14},
  doi              = {10.1103/PhysRevD.99.083504},
  eprint           = {1901.03321},
  file             = {:Lagos2019.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {astro-ph.CO},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
}

@Article{Enqvist2007,
  author           = {Kari Enqvist},
  journal          = {Gen.Rel.Grav.40:451-466,2008},
  title            = {Lemaitre-Tolman-Bondi model and accelerating expansion},
  year             = {2007},
  month            = sep,
  abstract         = {I discuss the spherically symmetric but inhomogeneous Lemaitre-Tolman- Bondi (LTB) metric, which provides an exact toy model for an inhomogeneous universe. Since we observe light rays from the past light cone, not the expansion of the universe, spatial variation in matter density and Hubble rate can have the same effect on redshift as acceleration in a perfectly homogeneous universe. As a consequence, a simple spatial variation in the Hubble rate can account for the distant supernova data in a dust universe without any dark energy. I also review various attempts towards a semirealistic description of the universe based on the LTB model.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:32:13},
  doi              = {10.1007/s10714-007-0553-9},
  eprint           = {0709.2044},
  file             = {:Enqvist2007.pdf:PDF},
  keywords         = {astro-ph},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {astro-ph},
}

@Article{GW190521-EM,
  author           = {M. J. Graham and K. E. S. Ford and B. McKernan and N. P. Ross and D. Stern and K. Burdge and M. Coughlin and S. G. Djorgovski and A. J. Drake and D. Duev and M. Kasliwal and A. A. Mahabal and S. van Velzen and J. Belicki and E. C. Bellm and R. Burruss and S. B. Cenko and V. Cunningham and G. Helou and S. R. Kulkarni and F. J. Masci and T. Prince and D. Reiley and H. Rodriguez and B. Rusholme and R. M. Smith and M. T. Soumagnac},
  journal          = {Phys. Rev. Lett. 124, 251102},
  title            = {Candidate Electromagnetic Counterpart to the Binary Black Hole Merger Gravitational Wave Event S190521g},
  year             = {2020},
  month            = jun,
  abstract         = {We report the first plausible optical electromagnetic (EM) counterpart to a (candidate) binary black hole (BBH) merger. Detected by the Zwicky Transient Facility (ZTF), the EM flare is consistent with expectations for a kicked BBH merger in the accretion disk of an active galactic nucleus (AGN), and is unlikely ($<O(0.01\%$)) due to intrinsic variability of this source. The lack of color evolution implies that it is not a supernovae and instead is strongly suggestive of a constant temperature shock. Other false-positive events, such as microlensing or a tidal disruption event, are ruled out or constrained to be $<O(0.1\%$). If the flare is associated with S190521g, we find plausible values of: total mass $ M_{\rm BBH} \sim 100 M_{\odot}$, kick velocity $v_k \sim 200\, {\rm km}\, {\rm s}^{-1}$ at $\theta \sim 60^{\circ}$ in a disk with aspect ratio $H/a \sim 0.01$ (i.e., disk height $H$ at radius $a$) and gas density $\rho \sim 10^{-10}\, {\rm g}\, {\rm cm}^{-3}$. The merger could have occurred at a disk migration trap ($a \sim 700\, r_{g}$; $r_g \equiv G M_{\rm SMBH} / c^2$, where $M_{\rm SMBH}$ is the mass of the AGN supermassive black hole). The combination of parameters implies a significant spin for at least one of the black holes in S190521g. The timing of our spectroscopy prevents useful constraints on broad-line asymmetry due to an off-center flare. We predict a repeat flare in this source due to a re-encountering with the disk in $\sim 1.6\, {\rm yr}\, (M_{\rm SMBH}/10^{8}M_{\odot})\, (a/10^{3}r_{g})^{3/2}$.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:33:34},
  doi              = {10.1103/PhysRevLett.124.251102},
  eprint           = {2006.14122},
  file             = {:GW190521-EM.pdf:PDF},
  groups           = {Observations},
  keywords         = {astro-ph.HE, astro-ph.GA},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {astro-ph.HE},
}

@Article{Goliath2001,
  author           = {M. Goliath and R. Amanullah and P. Astier and A. Goobar and R. Pain},
  journal          = {Astronomy {\&} Astrophysics},
  title            = {Supernovae and the nature of the dark energy},
  year             = {2001},
  month            = {dec},
  number           = {1},
  pages            = {6--18},
  volume           = {380},
  abstract         = {The use of Type Ia supernovae as calibrated standard candles is one of the most powerful tools to study the expansion history of the universe and thereby its energy components. While the analysis of some ~50 supernovae at redshifts around z~0.5 have provided strong evidence for an energy component with negative pressure, ``dark energy'', more data is needed to enable an accurate estimate of the amount and nature of this energy. This might be accomplished by a dedicated space telescope, the SuperNova / Acceleration Probe (2000; SNAP), which aims at collecting a large number of supernovae with z<2. In this paper we assess the ability of the SNAP mission to determine various properties of the ``dark energy.'' To exemplify, we expect SNAP, if operated for three years to study Type Ia supernovae, to be able to determine the parameters in a linear equation of state w(z)=w0 + w1 z to within a statistical uncertainty of +-0.04 for w0 and +0.15,-0.17 for w1 assuming that the universe is known to be flat and an independent high precision (sigma_{Omega_m}=0.015) measurement of the mass density Omega_m, is used to constrain the fit. An additional improvement can be obtained if a large number of low-z, as well as high-z, supernovae are included in the sample.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:35:36},
  doi              = {10.1051/0004-6361:20011398},
  eprint           = {astro-ph/0104009},
  file             = {:Goliath2001.pdf:PDF},
  groups           = {Observations, SNIa},
  keywords         = {astro-ph},
  modificationdate = {2022-03-21T22:09:57},
  primaryclass     = {astro-ph},
  publisher        = {{EDP} Sciences},
}

@Article{Barros2020,
  author           = {Bruno J. Barros and Tiago Barreiro and Tomi Koivisto and Nelson J. Nunes},
  journal          = {Physics of the Dark Universe},
  title            = {{Testing $F(Q)$ gravity with redshift space distortions}},
  year             = {2020},
  month            = {dec},
  pages            = {100616},
  volume           = {30},
  abstract         = {A Bayesian statistical analysis using redshift space distortions data is performed to test a model of Symmetric Teleparallel Gravity where gravity is non-metrical. The cosmological background mimics a $\Lambda$CDM evolution but differences arise in the perturbations. The linear matter fluctuations are numerically evolved and the study of the growth rate of structures is analysed in this cosmological setting. The best fit parameters reveal that the $\sigma_8$ tension between Planck and Large Scale Structure data can be alleviated within this framework.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:41:11},
  doi              = {10.1016/j.dark.2020.100616},
  eprint           = {2004.07867},
  file             = {:Barros2020.pdf:PDF},
  groups           = {f(Q)},
  keywords         = {gr-qc, astro-ph.CO},
  modificationdate = {2022-04-03T11:35:54},
  primaryclass     = {gr-qc},
  priority         = {prio3},
  publisher        = {Elsevier {BV}},
  readstatus       = {skimmed},
}

@Article{Anagnostopoulos2021,
  author           = {Fotios K. Anagnostopoulos and Spyros Basilakos and Emmanuel N. Saridakis},
  title            = {First evidence that non-metricity f(Q) gravity could challenge $\Lambda$CDM},
  year             = {2021},
  issn             = {0370-2693},
  month            = apr,
  pages            = {136634},
  volume           = {822},
  abstract         = {We propose a novel model in the framework of $f(Q)$ gravity, which is a gravitational modification class arising from the incorporation of non-metricity. The model has General Relativity as a particular limit, it has the same number of free parameters to those of $\Lambda$CDM, however at a cosmological framework it gives rise to a scenario that does not have $\Lambda$CDM as a limit. Nevertheless, confrontation with observations at both background and perturbation levels, namely with Supernovae type Ia (SNIa), Baryonic Acoustic Oscillations (BAO), cosmic chronometers (CC), and Redshift Space Distortion (RSD) data, reveals that the scenario, according to AIC, BIC and DIC information criteria, is in some datasets slightly preferred comparing to $\Lambda$CDM cosmology, although in all cases the two models are statistically indiscriminate. Finally, the model does not exhibit early dark energy features, and thus it immediately passes BBN constraints, while the variation of the effective Newton's constant lies well inside the observational bounds.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:41:44},
  doi              = {10.1016/j.physletb.2021.136634},
  eprint           = {2104.15123},
  file             = {:Anagnostopoulos2021.pdf:PDF},
  groups           = {f(Q)},
  keywords         = {gr-qc, astro-ph.CO, hep-th},
  modificationdate = {2022-04-03T11:37:16},
  primaryclass     = {gr-qc},
  priority         = {prio3},
  readstatus       = {read},
}

@Article{Jimenez2017,
  author           = {Jose Beltran Jimenez and Lavinia Heisenberg and Tomi Koivisto},
  journal          = {Phys. Rev. D 98, 044048 (2018)},
  title            = {Coincident General Relativity},
  year             = {2017},
  month            = oct,
  abstract         = {The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter is discovered an exceptional class which is consistent with a vanishing affine connection. Based on this remarkable property, this work proposes a simpler geometrical formulation of General Relativity that is oblivious to the affine spacetime structure, thus fundamentally depriving gravity of any inertial character. The resulting theory is described by the Hilbert action purged from the boundary term and is more robustly underpinned by the spin-2 field theory, where an extra symmetry is now manifest, possibly related to the double copy structure of the gravity amplitudes. This construction also provides a novel starting point for modified gravity theories, and the paper presents new and simple generalisations where analytical self-accelerating cosmological solutions arise naturally in the early and late time universe.},
  archiveprefix    = {arXiv},
  comment          = {Artigo referenciado pelo Barros2020 com contas, mas acho que não era preciso pois Jimenez2019 tem tudo o que é preciso},
  creationdate     = {2022-01-08T18:43:08},
  doi              = {10.1103/PhysRevD.98.044048},
  eprint           = {1710.03116},
  file             = {:Jimenez2017.pdf:PDF},
  keywords         = {gr-qc, astro-ph.CO, hep-th},
  modificationdate = {2022-03-21T21:46:38},
  primaryclass     = {gr-qc},
}

@Article{Jimenez2019,
  author           = {Jose Beltrán Jiménez and Lavinia Heisenberg and Tomi Sebastian Koivisto and Simon Pekar},
  journal          = {Phys. Rev. D 101, 103507 (2020)},
  title            = {Cosmology in $f(Q)$ geometry},
  year             = {2019},
  month            = jun,
  abstract         = {The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of General Relativity \`a la Einstein attributes gravity to the spacetime curvature, to which we have grown accustomed. However, this perception has masked the fact that two alternative, though equivalent, formulations of General Relativity in flat spacetimes exist, where gravity can be fully ascribed either to torsion or to non-metricity. The latter allows a simpler geometrical formulation of General Relativity that is oblivious to the affine spacetime structure. Generalisations along this line permit to generate teleparallel and symmetric teleparallel theories of gravity with exceptional properties. In this work we explore modified gravity theories based on non-linear extensions of the non-metricity scalar. After presenting some general properties and briefly studying some interesting background cosmologies (including accelerating solutions with relevance for inflation and dark energy), we analyse the behaviour of the cosmological perturbations. Tensor perturbations feature a re-scaling of the corresponding Newton's constant, while vector perturbations do not contribute in the absence of vector sources. In the scalar sector we find two additional propagating modes, hinting that $f(Q)$ theories introduce, at least, two additional degrees of freedom. These scalar modes disappear around maximally symmetric backgrounds because of the appearance of an accidental residual gauge symmetry corresponding to a restricted diffeomorphism. We finally discuss the potential strong coupling problems of these maximally symmetric backgrounds caused by the discontinuity in the number of propagating modes.},
  archiveprefix    = {arXiv},
  comment          = {Artigo onde o Barros2020 foi buscar a maior parte das contas},
  creationdate     = {2022-01-08T18:43:32},
  doi              = {10.1103/PhysRevD.101.103507},
  eprint           = {1906.10027},
  file             = {:Jimenez2019.pdf:PDF},
  groups           = {f(Q), Dynamical Systems},
  keywords         = {gr-qc, astro-ph.CO, hep-th},
  modificationdate = {2022-04-26T12:27:36},
  primaryclass     = {gr-qc},
  priority         = {prio3},
  readstatus       = {skimmed},
}

@Article{Jimenez2019a,
  author           = {Jose Beltr{\'{a}}n Jim{\'{e}}nez and Lavinia Heisenberg and Tomi Koivisto},
  journal          = {Universe},
  title            = {The Geometrical Trinity of Gravity},
  year             = {2019},
  month            = {jul},
  number           = {7},
  pages            = {173},
  volume           = {5},
  abstract         = {The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the spacetime curvature, which is now the standard interpretation of gravity. However, this is not the only possibility. In these notes we discuss two alternative, though equivalent, formulations of General Relativity in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity, thus putting forward the existence of three seemingly unrelated representations of the same underlying theory. Based on these three alternative formulations of General Relativity, we then discuss some extensions.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:43:55},
  doi              = {10.3390/universe5070173},
  eprint           = {1903.06830},
  file             = {:Trinity.pdf:PDF},
  keywords         = {hep-th, gr-qc},
  modificationdate = {2022-03-21T22:21:48},
  primaryclass     = {hep-th},
  priority         = {prio3},
  publisher        = {{MDPI} {AG}},
}

@Article{Khyllep2021,
  author           = {Wompherdeiki Khyllep and Andronikos Paliathanasis and Jibitesh Dutta},
  journal          = {Phys. Rev. D 103, 103521 (2021)},
  title            = {Cosmological solutions and growth index of matter perturbations in $f(Q)$ gravity},
  year             = {2021},
  month            = mar,
  abstract         = {The present work studies one of Einstein's alternative formulations based on the non-metricity scalar $Q$ generalized as $f(Q)$ theory. More specifically, we consider the power-law form of $f(Q)$ gravity i.e. $f(Q)=Q+\alpha\, Q^n$. Here, we analyze the behavior of the cosmological model at the background and perturbation level. At the background level, we find the effective evolution of the model is the same as that of the $\Lambda$CDM for $|n|<1$. Interestingly, the geometric component of the theory solely determined the late-time acceleration of the Universe. We also examine the integrability of the model by employing the method of singularity analysis. In particular, we find the conditions under which field equations pass the Painlev\'{e} test and hence possess the Painlev\'{e} property. While the equations pass the Painlev\'{e} test in the presence of dust for any value of $n$, the test is valid after the addition of radiation fluid only for $n<1$. Finally, at the perturbation level, the behavior of matter growth index signifies a deviation of the model from the $\Lambda$CDM even for $|n|<1$.},
  archiveprefix    = {arXiv},
  comment          = {Análise de um modelo de f(Q) da forma f(Q) = Q + αQ<sup>n</sup>},
  creationdate     = {2022-01-08T18:45:32},
  doi              = {10.1103/PhysRevD.103.103521},
  eprint           = {2103.08372},
  file             = {:Khyllep2021.pdf:PDF},
  groups           = {f(Q)},
  keywords         = {gr-qc, hep-ph, nlin.CD},
  modificationdate = {2022-03-21T21:47:28},
  primaryclass     = {gr-qc},
  priority         = {prio3},
}

@Article{Lazkoz2019,
  author           = {Ruth Lazkoz and Francisco S. N. Lobo and María Ortiz-Baños and Vincenzo Salzano},
  journal          = {Physical Review D},
  title            = {Observational constraints of $f(Q)$ gravity},
  year             = {2019},
  month            = {nov},
  number           = {10},
  pages            = {104027},
  volume           = {100},
  abstract         = {In this work, we consider an extension of symmetric teleparallel gravity, namely, $f(Q)$ gravity, where the fundamental block to describe spacetime is the nonmetricity, $Q$. Within this formulation of gravitation, we perform an observational analysis of several modified $f(Q)$ models using the redshift approach, where the $f(Q)$ Lagrangian is reformulated as an explicit function of the redshift, $f(z)$. Various different polynomial parameterizations of $f(z)$ are proposed, including new terms which would allow for deviations from the $\Lambda$CDM model. Given a variety of observational probes, such as the expansion rate data from early-type galaxies, Type Ia Supernovae, Quasars, Gamma Ray Bursts, Baryon Acoustic Oscillations data and Cosmic Microwave Background distance priors, we have checked the validity of these models at the background level in order to verify if this new formalism provides us with plausible alternative models to explain the late time acceleration of the universe. Indeed, this novel approach provides a different perspective on the formulation of observationally reliable alternative models of gravity.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:46:18},
  doi              = {10.1103/physrevd.100.104027},
  eprint           = {1907.13219},
  file             = {:Lazkoz2019.pdf:PDF},
  groups           = {f(Q)},
  keywords         = {gr-qc, astro-ph.CO},
  modificationdate = {2022-03-22T13:58:13},
  primaryclass     = {gr-qc},
  priority         = {prio3},
  publisher        = {American Physical Society ({APS})},
}

@Article{Atayde2021,
  author           = {Luís Atayde and Noemi Frusciante},
  journal          = {Phys.Rev.D 104 (2021) 6, 064052},
  title            = {Can $f(Q)$ gravity challenge $\Lambda$CDM?},
  year             = {2021},
  month            = aug,
  abstract         = {We study observational constraints on the non-metricity $f(Q)$-gravity which reproduces an exact $\Lambda$CDM background expansion history while modifying the evolution of linear perturbations. To this purpose we use Cosmic Microwave Background (CMB) radiation, baryonic acoustic oscillations (BAO), redshift-space distortions (RSD), supernovae type Ia (SNIa), galaxy clustering (GC) and weak gravitational lensing (WL) measurements. We set stringent constraints on the parameter of the model controlling the modifications to the gravitational interaction at linear perturbation level. We find the model to be statistically preferred by data over the $\Lambda$CDM according to the $\chi^2$ and deviance information criterion statistics for the combination with CMB, BAO, RSD and SNIa. This is mostly associated to a better fit to the low-$\ell$ tail of CMB temperature anisotropies.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:46:48},
  doi              = {10.1103/PhysRevD.104.064052},
  eprint           = {2108.10832},
  file             = {:Atayde2021.pdf:PDF},
  groups           = {f(Q)},
  keywords         = {astro-ph.CO, gr-qc},
  modificationdate = {2022-03-21T18:01:23},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
}

@Article{Frusciante2021,
  author           = {Noemi Frusciante},
  journal          = {Physical Review D},
  title            = {Signatures of $f(Q)$-gravity in cosmology},
  year             = {2021},
  month            = {feb},
  number           = {4},
  pages            = {044021},
  volume           = {103},
  abstract         = {We investigate the impact on cosmological observables of $f(Q)$-gravity, a specific class of modified gravity models in which gravity is described by the non-metricity scalar, $Q$. In particular we focus on a specific model which is indistinguishable from the $\Lambda$-cold-dark-matter ($\Lambda$CDM) model at the background level, while showing peculiar and measurable signatures at linear perturbation level. These are attributed to a time-dependent Planck mass and are regulated by a single dimensionless parameter, $\alpha$. In comparison to the $\Lambda$CDM model, we find for positive values of $\alpha$ a suppressed matter power spectrum and lensing effect on the Cosmic Microwave Background radiation (CMB) angular power spectrum and an enhanced integrated-Sachs-Wolfe tail of CMB temperature anisotropies. The opposite behaviors are present when the $\alpha$ parameter is negative. We also investigate the modified Gravitational Waves (GWs) propagation and show the prediction of the GWs luminosity distance compared to the standard electromagnetic one. Finally, we infer the accuracy on the free parameter of the model with standard sirens at future GWs detectors.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:47:12},
  doi              = {10.1103/physrevd.103.044021},
  eprint           = {2101.09242},
  file             = {:Frusciante2021.pdf:PDF},
  groups           = {f(Q)},
  keywords         = {astro-ph.CO, gr-qc},
  modificationdate = {2022-03-21T21:59:20},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
  publisher        = {American Physical Society ({APS})},
}

@Article{Harko2018,
  author           = {Tiberiu Harko and Tomi S. Koivisto and Francisco S. N. Lobo and Gonzalo J. Olmo and Diego Rubiera-Garcia},
  journal          = {Phys. Rev. D 98, 084043 (2018)},
  title            = {Coupling matter in modified $Q$-gravity},
  year             = {2018},
  month            = jun,
  abstract         = {We present a novel theory of gravity by considering an extension of symmetric teleparallel gravity. This is done by introducing, in the framework of the metric-affine formalism, a new class of theories where the nonmetricity $Q$ is nonminimally coupled to the matter Lagrangian. More specifically, we consider a Lagrangian of the form $L \sim f_1(Q) + f_2(Q) L_M$, where $f_1$ and $f_2$ are generic functions of $Q$, and $L_M$ is the matter Lagrangian. This nonminimal coupling entails the nonconservation of the energy-momentum tensor, and consequently the appearance of an extra force. The motivation is to verify whether the subtle improvement of the geometrical formulation, when implemented in the matter sector, would allow more universally consistent and viable realisations of the nonminimal curvature-matter coupling theories. Furthermore, we consider several cosmological applications by presenting the evolution equations and imposing specific functional forms of the functions $f_1(Q)$ and $f_2(Q)$, such as power-law and exponential dependencies of the nonminimal couplings. Cosmological solutions are considered in two general classes of models, and found to feature accelerating expansion at late times.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:47:50},
  doi              = {10.1103/PhysRevD.98.084043},
  eprint           = {1806.10437},
  file             = {:Harko2018.pdf:PDF},
  keywords         = {gr-qc, astro-ph.CO, hep-th},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {gr-qc},
}

@Article{Xu2019,
  author           = {Yixin Xu and Guangjie Li and Tiberiu Harko and Shi-Dong Liang},
  journal          = {The European Physical Journal C 79, 708 (2019)},
  title            = {$f(Q,T)$ gravity},
  year             = {2019},
  month            = aug,
  abstract         = {We propose an extension of the symmetric teleparallel gravity, in which the gravitational action $L$ is given by an arbitrary function $f$ of the nonmetricity $Q$ and of the trace of the matter energy-momentum tensor $T$, so that $L=f(Q,T)$. The field equations of the theory are obtained by varying the gravitational action with respect to both metric and connection. The covariant divergence of the field equations is obtained, with the geometry-matter coupling leading to the nonconservation of the energy-momentum tensor. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of general relativity. We consider several cosmological models by imposing some simple functional forms of the function $f(Q,T)$, corresponding to additive expressions of $f(Q,T)$ of the form $f(Q,T)=\alpha Q+\beta T$, $f(Q,T)=\alpha Q^{n+1}+\beta T$, and $f(Q,T)=-\alpha Q-\beta T^2$. The Hubble function, the deceleration parameter, and the matter energy density are obtained as a function of the redshift by using analytical and numerical techniques. For all considered cases the Universe experiences an accelerating expansion, ending with a de Sitter type evolution. The theoretical predictions are also compared with the results of the standard $\Lambda$CDM model.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T18:48:29},
  doi              = {10.1140/epjc/s10052-019-7207-4},
  eprint           = {1908.04760},
  file             = {:Xu2019.pdf:PDF},
  keywords         = {gr-qc, hep-th},
  modificationdate = {2022-01-25T17:20:55},
  primaryclass     = {gr-qc},
}

@Article{GeneralizationsGR-R2018,
  author           = {Lavinia Heisenberg},
  title            = {A systematic approach to generalisations of General Relativity and their cosmological implications},
  year             = {2018},
  month            = jul,
  abstract         = {A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious challenges of modern cosmology and of particle physics have motivated the exploration of further generalised theories of spacetime. Even though Einstein's interpretation of gravity in terms of the curvature of spacetime is commonly adopted, the assignment of geometrical concepts to gravity is ambiguous because General Relativity allows three entirely different, but equivalent approaches of which Einstein's interpretation is only one. From a field-theoretical perspective, however, the construction of a consistent theory for a Lorentz-invariant massless spin-2 particle uniquely leads to General Relativity. Keeping Lorentz invariance then implies that any modification of General Relativity will inevitably introduce additional propagating degrees of freedom into the gravity sector. Adopting this perspective, we will review the recent progress in constructing consistent field theories of gravity based on additional scalar, vector and tensor fields. Within this conceptual framework, we will discuss theories with Galileons, with Lagrange densities as constructed by Horndeski and beyond, extended to DHOST interactions, or containing generalized Proca fields and extensions thereof, or several Proca fields, as well as bigravity theories and scalar-vector-tensor theories. We will review the motivation of their inception, different formulations, and essential results obtained within these classes of theories together with their empirical viability.},
  archiveprefix    = {arXiv},
  comment          = {A big review on several modifications to GR, with a small chapter dedicated to the different interpretations of gravity},
  creationdate     = {2022-01-08T21:46:44},
  doi              = {10.1016/j.physrep.2018.11.006},
  eprint           = {1807.01725},
  file             = {:GeneralizationsGR-R2018.pdf:PDF},
  groups           = {Review},
  keywords         = {gr-qc, astro-ph.CO, hep-th},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {gr-qc},
  priority         = {prio3},
}

@Article{GetDist,
  author           = {Antony Lewis},
  title            = {GetDist: a Python package for analysing Monte Carlo samples},
  year             = {2019},
  month            = oct,
  abstract         = {Monte Carlo techniques, including MCMC and other methods, are widely used and generate sets of samples from a parameter space of interest that can be used to infer or plot quantities of interest. This note outlines methods used the Python GetDist package to calculate marginalized one and two dimensional densities using Kernel Density Estimation (KDE). Many Monte Carlo methods produce correlated and/or weighted samples, for example produced by MCMC, nested, or importance sampling, and there can be hard boundary priors. GetDist's baseline method consists of applying a linear boundary kernel, and then using multiplicative bias correction. The smoothing bandwidth is selected automatically following Botev et al., based on a mixture of heuristics and optimization results using the expected scaling with an effective number of samples (defined to account for MCMC correlations and weights). Two-dimensional KDE use an automatically-determined elliptical Gaussian kernel for correlated distributions. The package includes tools for producing a variety of publication-quality figures using a simple named-parameter interface, as well as a graphical user interface that can be used for interactive exploration. It can also calculate convergence diagnostics, produce tables of limits, and output in latex.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-08T22:00:02},
  eprint           = {1910.13970},
  file             = {:GetDist.pdf:PDF},
  groups           = {Software},
  keywords         = {astro-ph.IM, astro-ph.CO, physics.data-an},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {astro-ph.IM},
}

@Article{Planck2018,
  author           = {Planck Collaboration},
  journal          = {Astronomy {\&} Astrophysics},
  title            = {Planck 2018 results},
  year             = {2020},
  month            = {sep},
  pages            = {A6},
  volume           = {641},
  creationdate     = {2022-01-09T11:49:49},
  doi              = {10.1051/0004-6361/201833910},
  file             = {:Planck2018.pdf:PDF},
  groups           = {Observations},
  modificationdate = {2022-01-25T17:20:55},
  publisher        = {{EDP} Sciences},
}

@Article{Teleparallel-R2021,
  author           = {Sebastian Bahamonde and Konstantinos F. Dialektopoulos and Celia Escamilla-Rivera and Gabriel Farrugia and Viktor Gakis and Martin Hendry and Manuel Hohmann and Jackson Levi Said and Jurgen Mifsud and Eleonora Di Valentino},
  title            = {Teleparallel Gravity: From Theory to Cosmology},
  year             = {2021},
  month            = jun,
  abstract         = {Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we relate this form of geometry to the broader metric-affine approach to forming gravitational theories where we describe a systematic way of constructing consistent teleparallel theories that respect certain physical conditions such as local Lorentz invariance. We first use teleparallel gravity to formulate a teleparallel equivalent of general relativity which is dynamically equivalent to general relativity but which may have different behaviors for other scenarios, such as quantum gravity. After setting this foundation, we describe the plethora of modified teleparallel theories of gravity that have been proposed in the literature. In the second part of the Review, we first survey works in teleparallel astrophysics literature where we focus on the open questions in this regime of physics. We then discuss the cosmological consequences for the various formulations of teleparallel gravity. We do this at background level by exploring works using various approaches ranging from dynamical systems to Noether symmetries, and more. Naturally, we then discuss perturbation theory, firstly by giving a concise approach in which this can be applied in teleparallel gravity theories and then apply it to a number of important theories in the literature. Finally, we examine works in observational and precision cosmology across the plethora of proposal theories. This is done using some of the latest observations and is used to tackle cosmological tensions which may be alleviated in teleparallel cosmology. We also introduce a number of recent works in the application of machine learning to gravity, we do this through deep learning and Gaussian processes, together with discussions about other approaches in the literature.},
  archiveprefix    = {arXiv},
  comment          = {A review, and some original work, regarding teleparallel gravity

Includes historical remarks regarding teleparallelism

Includes some nice figures to visualize the different equivalent representations of gravity},
  creationdate     = {2022-01-11T18:16:20},
  eprint           = {2106.13793},
  file             = {:Teleparallel-R2021.pdf:PDF},
  groups           = {Review},
  keywords         = {gr-qc, astro-ph.CO},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {gr-qc},
  priority         = {prio3},
}

@Article{Conroy2017,
  author           = {Aindriú Conroy and Tomi Koivisto},
  title            = {The spectrum of symmetric teleparallel gravity},
  year             = {2017},
  month            = oct,
  abstract         = {General Relativity and its higher derivative extensions have symmetric teleparallel reformulations in terms of the non-metricity tensor within a torsion-free and flat geometry. These notes present a derivation of the exact propagator for the most general infinite-derivative, even-parity and generally covariant theory in the symmetric teleparallel spacetime. The action made up of the non-metricity tensor and its contractions is decomposed into terms involving the metric and a gauge vector field and is found to complement the previously known non-local ghost- and singularity-free theories.},
  archiveprefix    = {arXiv},
  comment          = {Includes cool diagramatic representation of the different possible spacetimes built with R, Q and T},
  creationdate     = {2022-01-11T18:24:20},
  doi              = {10.1140/epjc/s10052-018-6410-z},
  eprint           = {1710.05708},
  file             = {:Conroy2017.pdf:PDF},
  keywords         = {gr-qc, hep-th},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {gr-qc},
}

@Article{Pantheon,
  author           = {D. M. Scolnic and D. O. Jones and A. Rest and Y. C. Pan and R. Chornock and R. J. Foley and M. E. Huber and R. Kessler and G. Narayan and A. G. Riess and S. Rodney and E. Berger and D. J. Brout and P. J. Challis and M. Drout and D. Finkbeiner and R. Lunnan and R. P. Kirshner and N. E. Sanders and E. Schlafly and S. Smartt and C. W. Stubbs and J. Tonry and W. M. Wood-Vasey and M. Foley and J. Hand and E. Johnson and W. S. Burgett and K. C. Chambers and P. W. Draper and K. W. Hodapp and N. Kaiser and R. P. Kudritzki and E. A. Magnier and N. Metcalfe and F. Bresolin and E. Gall and R. Kotak and M. McCrum and K. W. Smith},
  title            = {The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample},
  year             = {2017},
  month            = oct,
  abstract         = {We present optical light curves, redshifts, and classifications for 365 spectroscopically confirmed Type Ia supernovae (SNe Ia) discovered by the Pan-STARRS1 (PS1) Medium Deep Survey. We detail improvements to the PS1 SN photometry, astrometry and calibration that reduce the systematic uncertainties in the PS1 SN Ia distances. We combine the subset of 279 PS1 SN Ia ($0.03 < z < 0.68$) with useful distance estimates of SN Ia from SDSS, SNLS, various low-z and HST samples to form the largest combined sample of SN Ia consisting of a total of 1048 SN Ia ranging from $0.01 < z < 2.3$, which we call the `Pantheon Sample'. When combining Planck 2015 CMB measurements with the Pantheon SN sample, we find $\Omega_m=0.307\pm0.012$ and $w = -1.026\pm0.041$ for the wCDM model. When the SN and CMB constraints are combined with constraints from BAO and local H0 measurements, the analysis yields the most precise measurement of dark energy to date: $w0 = -1.007\pm 0.089$ and $wa = -0.222 \pm0.407$ for the w0waCDM model. Tension with a cosmological constant previously seen in an analysis of PS1 and low-z SNe has diminished after an increase of $2\times$ in the statistics of the PS1 sample, improved calibration and photometry, and stricter light-curve quality cuts. We find the systematic uncertainties in our measurements of dark energy are almost as large as the statistical uncertainties, primarily due to limitations of modeling the low-redshift sample. This must be addressed for future progress in using SN Ia to measure dark energy.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-11T18:31:17},
  doi              = {10.3847/1538-4357/aab9bb},
  eprint           = {1710.00845},
  file             = {:Pantheon.pdf:PDF},
  groups           = {SNIa, Observations},
  keywords         = {astro-ph.CO},
  modificationdate = {2022-01-25T17:20:55},
  primaryclass     = {astro-ph.CO},
}

@Misc{Pantheon-repo,
  author           = {D. M. Scolnic and D. O. Jones and A. Rest and Y. C. Pan and R. Chornock and R. J. Foley and M. E. Huber and R. Kessler and G. Narayan and A. G. Riess and S. Rodney and E. Berger and D. J. Brout and P. J. Challis and M. Drout and D. Finkbeiner and R. Lunnan and R. P. Kirshner and N. E. Sanders and E. Schlafly and S. Smartt and C. W. Stubbs and J. Tonry and W. M. Wood-Vasey and M. Foley and J. Hand and E. Johnson and W. S. Burgett and K. C. Chambers and P. W. Draper and K. W. Hodapp and N. Kaiser and R. P. Kudritzki and E. A. Magnier and N. Metcalfe and F. Bresolin and E. Gall and R. Kotak and M. McCrum and K. W. Smith},
  title            = {Pantheon analysis repository},
  creationdate     = {2022-01-11T19:34:17},
  groups           = {SNIa, Observations},
  modificationdate = {2022-01-25T17:20:55},
  url              = {https://github.com/dscolnic/Pantheon},
}

@Article{GWTC-3,
  author           = {The LIGO Scientific Collaboration and the Virgo Collaboration and the KAGRA Collaboration},
  title            = {GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run},
  year             = {2021},
  month            = nov,
  abstract         = {The third Gravitational-wave Transient Catalog (GWTC-3) describes signals detected with Advanced LIGO and Advanced Virgo up to the end of their third observing run. Updating the previous GWTC-2.1, we present candidate gravitational waves from compact binary coalescences during the second half of the third observing run (O3b) between 1 November 2019, 15:00 UTC and 27 March 2020, 17:00 UTC. There are 35 compact binary coalescence candidates identified by at least one of our search algorithms with a probability of astrophysical origin $p_\mathrm{astro} > 0.5$. Of these, 18 were previously reported as low-latency public alerts, and 17 are reported here for the first time. Based upon estimates for the component masses, our O3b candidates with $p_\mathrm{astro} > 0.5$ are consistent with gravitational-wave signals from binary black holes or neutron star-black hole binaries, and we identify none from binary neutron stars. However, from the gravitational-wave data alone, we are not able to measure matter effects that distinguish whether the binary components are neutron stars or black holes. The range of inferred component masses is similar to that found with previous catalogs, but the O3b candidates include the first confident observations of neutron star-black hole binaries. Including the 35 candidates from O3b in addition to those from GWTC-2.1, GWTC-3 contains 90 candidates found by our analysis with $p_\mathrm{astro} > 0.5$ across the first three observing runs. These observations of compact binary coalescences present an unprecedented view of the properties of black holes and neutron stars.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-11T22:28:28},
  eprint           = {2111.03606},
  file             = {:GWTC-3.pdf:PDF},
  groups           = {Observations},
  keywords         = {gr-qc, astro-ph.HE},
  modificationdate = {2022-01-25T17:20:56},
  primaryclass     = {gr-qc},
}

@Book{Inverno,
  author           = {Inverno, Ray},
  publisher        = {Clarendon Press Oxford University Press},
  title            = {Introducing Einstein's relativity},
  year             = {1992},
  address          = {Oxford England New York},
  isbn             = {9780198596868},
  creationdate     = {2022-01-11T22:51:04},
  file             = {:Inverno.pdf:PDF},
  groups           = {Books},
  modificationdate = {2022-01-25T17:20:48},
  priority         = {prio3},
}

@Article{Baumann,
  author           = {Daniel Baumann},
  journal          = {Part III Mathematical Tripos},
  title            = {Cosmology},
  year             = {2012},
  creationdate     = {2022-01-11T22:53:45},
  file             = {:Baumann.pdf:PDF},
  groups           = {Books},
  modificationdate = {2022-01-25T17:20:48},
  priority         = {prio3},
}

@Book{Dodelson,
  author           = {Dodelson, Scott},
  publisher        = {Academic Press, An Imprint of Elsevier},
  title            = {Modern cosmology},
  year             = {2003},
  address          = {San Diego, California},
  isbn             = {9780122191411},
  creationdate     = {2022-01-11T23:15:51},
  file             = {:Dodelson.pdf:PDF},
  groups           = {Books},
  modificationdate = {2022-01-25T17:20:48},
  priority         = {prio3},
}

@Article{Ayuso2020,
  author           = {Ismael Ayuso and Ruth Lazkoz and Vincenzo Salzano},
  journal          = {Phys. Rev. D 103, 063505 (2021)},
  title            = {Observational constraints on cosmological solutions of $f(Q)$ theories},
  year             = {2020},
  month            = nov,
  abstract         = {Over the last years some interest has been gathered by $f(Q)$ theories, which are new candidates to replace Einstein's prescription for gravity. The non-metricity tensor $Q$ allows to put forward the assumption of a free torsionless connection and, consequently, new degrees of freedom in the action are taken into account. This work focuses on a class of $f(Q)$ theories, characterized by the presence of a general power-law term which adds up to the standard (linear in) $Q$ term in the action, and on new cosmological scenarios arising from them. Using the Markov chain Montecarlo method we carry out statistical tests relying upon background data such as Type Ia Supernovae luminosities and direct Hubble data (from cosmic clocks), along with Cosmic Microwave Background shift and Baryon Acoustic Oscillations data. This allows us to perform a multifaceted comparison between these new cosmologies and the (concordance) $\Lambda$CDM setup. We conclude that, at the current precision level, the best fits of our $f(Q)$ models correspond to values of their specific parameters which make them hardly distinguishable from our General Relativity "\'echantillon", that is $\Lambda$CDM.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-11T23:29:53},
  doi              = {10.1103/PhysRevD.103.063505},
  eprint           = {2012.00046},
  file             = {:Ayuso2020.pdf:PDF},
  groups           = {f(Q)},
  keywords         = {astro-ph.CO, gr-qc, hep-th},
  modificationdate = {2022-02-08T15:03:31},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
}

@Article{Belgacem2019a,
  author           = {Enis Belgacem and Yves Dirian and Stefano Foffa and Eric J. Howell and Michele Maggiore and Tania Regimbau},
  title            = {Cosmology and dark energy from joint gravitational wave-GRB observations},
  year             = {2019},
  month            = jul,
  abstract         = {Gravitational-wave (GW) detectors can contribute to the measurement of cosmological parameters and to testing the dark-energy sector of alternatives to $\Lambda$CDM, by using standard sirens. In this paper we focus on binary neutron stars with a counterpart detected through a gamma-ray burst (GRB), both at a second-generation network made by advanced LIGO+advanced Virgo+LIGO India+Kagra, and at third-generation (3G) detectors, discussing in particular the cases of a single Einstein Telescope (ET), and of a network of ET plus two Cosmic Explorer (CE). We construct mock catalogs of standard sirens, using different scenarios for the local merger rate and for the detection of the electromagnetic counterpart. For 3G detectors we estimate the coincidences with a GRB detector with the characteristics of the proposed THESEUS mission. We discuss how these standard sirens with a GRB counterpart can improve the determination of cosmological parameters (and particularly of $H_0$) in $\Lambda$CDM, and we then study how to extract information on dark energy, considering both a non-trivial dark energy equation of state and modified GW propagation. We find that a 2G detector network can already reach, over several years of data taking, an interesting sensitivity to modified GW propagation, while a single ET detector would have a remarkable potential for discovery. We also find that, to fully exploit the potential of a ET+CE+CE network, it is necessary a much stronger program of search for electromagnetic counterparts (or else to resort to statistical methods for standard sirens), and furthermore gravitational lensing can become a limiting factor.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-11T23:31:48},
  doi              = {10.1088/1475-7516/2019/08/015},
  eprint           = {1907.01487},
  file             = {:Belgacem2019a.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {astro-ph.CO},
  modificationdate = {2022-01-25T17:20:48},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
}

@Article{Belgacem2017a,
  author           = {Enis Belgacem and Yves Dirian and Stefano Foffa and Michele Maggiore},
  journal          = {Phys. Rev. D 97, 104066 (2018)},
  title            = {The gravitational-wave luminosity distance in modified gravity theories},
  year             = {2017},
  month            = dec,
  abstract         = {In modified gravity the propagation of gravitational waves (GWs) is in general different from that in general relativity. As a result, the luminosity distance for GWs can differ from that for electromagnetic signals, and is affected both by the dark energy equation of state $w_{\rm DE}(z)$ and by a function $\delta(z)$ describing modified propagation. We show that the effect of modified propagation in general dominates over the effect of the dark energy equation of state, making it easier to distinguish a modified gravity model from $\Lambda$CDM. We illustrate this using a nonlocal modification of gravity, that has been shown to fit remarkably well CMB, SNe, BAO and structure formation data, and we discuss the prospects for distinguishing nonlocal gravity from $\Lambda$CDM with the Einstein Telescope. We find that, depending on the exact sensitivity, a few tens of standard sirens with measured redshift at $z\sim 0.4$, or a few hundreds at $1 < z < 2$, could suffice.},
  archiveprefix    = {arXiv},
  comment          = {Modificação à distância luminosa de ondas gravitacionais ao realizar perturbações tensoriais arbitrárias.
<b>Assume o estado do universo, por isso pode não ser sempre válido!</b>},
  creationdate     = {2022-01-11T23:34:18},
  doi              = {10.1103/PhysRevD.97.104066},
  eprint           = {1712.08108},
  file             = {:Belgacem2017a.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {astro-ph.CO, gr-qc, hep-th},
  modificationdate = {2022-01-27T23:23:21},
  primaryclass     = {astro-ph.CO},
  priority         = {prio2},
  readstatus       = {skimmed},
}

@Misc{PyStan,
  author           = {Riddell, Allen and Hartikainen, Ari and Carter, Matthew},
  howpublished     = {PyPi},
  month            = mar,
  title            = {pystan (3.0.0)},
  year             = {2021},
  creationdate     = {2022-01-12T10:45:41},
  groups           = {Software},
  modificationdate = {2022-01-25T17:20:55},
}

@Manual{Stan,
  title            = {Stan Modeling Language Users Guide and Reference Manual},
  author           = {Stan Development Team},
  edition          = {2.28},
  year             = {2021},
  creationdate     = {2022-01-12T10:48:04},
  groups           = {Software},
  modificationdate = {2022-01-25T17:20:55},
  url              = {https://mc-stan.org},
}

@Book{MGCosmology2021,
  editor           = {Emmanuel N. Saridakis and Ruth Lazkoz and Vincenzo Salzano and Paulo Vargas Moniz and Salvatore Capozziello and Jose Beltrán Jiménez and Mariafelicia De Laurentis and Gonzalo J. Olmo},
  publisher        = {Springer International Publishing},
  title            = {Modified Gravity and Cosmology},
  year             = {2021},
  month            = dec,
  creationdate     = {2022-01-24T16:32:00},
  ean              = {9783030837150},
  file             = {:MG&Cosmology2021.pdf:PDF},
  groups           = {Books},
  modificationdate = {2022-03-21T22:08:52},
  pagetotal        = {629},
  priority         = {prio3},
  url              = {https://www.ebook.de/de/product/42071306/modified_gravity_and_cosmology.html},
}

@Article{Salako2013,
  author           = {I. G. Salako and M. E. Rodrigues and A. V. Kpadonou and M. J. S. Houndjo and J. Tossa},
  journal          = {JCAP 060, 1475-7516 (2013)},
  title            = {LCDM Model in f(T) Gravity: Reconstruction, Thermodynamics and Stability},
  year             = {2013},
  month            = jun,
  abstract         = {We investigate some cosmological features of the LCDM model in the framework of the generalized teleparallel theory of gravity f(T) where T denotes the torsion scalar. Its reconstruction is performed giving rise to an integration constant Q and other input parameters according to which we point out more analysis. Thereby, we show that for some values of this constant, the first and second laws of thermodynamics can be realized in the equilibrium description, for the universe with the temperature inside the horizon equal to that at the apparent horizon. Moreover, still within these suitable values of the constant, we show that the model may be stable using the de Sitter and Power-Law cosmological solutions.},
  archiveprefix    = {arXiv},
  comment          = {Primeiro artigo que encontrei sobre f(T) já não sei bem onde, não tem grande informação no que toca a dedução do modelo e nada sobre perturbações tensoriais, apenas apresenta 1 página interessante onde dizem qual o modelo mais geral que replica ΛCDM e algumas referências onde o mesmo foi estudado.},
  creationdate     = {2022-01-24T19:27:52},
  doi              = {10.1088/1475-7516/2013/11/060},
  eprint           = {1307.0730},
  file             = {:Salako2013.pdf:PDF},
  groups           = {f(T)},
  keywords         = {gr-qc},
  modificationdate = {2022-02-08T15:03:44},
  primaryclass     = {gr-qc},
  priority         = {prio2},
  readstatus       = {read},
}

@Article{Fay2007,
  author           = {Stephane Fay and Savvas Nesseris and Leandros Perivolaropoulos},
  title            = {Can f(R) modified gravity theories mimic a ΛCDM cosmology?},
  year             = {2007},
  issn             = {1550-2368},
  volume           = {76},
  abstract         = {We consider f(R) modified gravity theories in the metric variation formalism and attempt to reconstruct the function f(R) by demanding a background LCDM cosmology. In particular we impose the following requirements: a. A background cosmic history H(z) provided by the usual flat LCDM parametrization though the radiation (w_eff=1/3), matter (w_eff=0) and deSitter (w_eff=-1) eras. b. Matter and radiation dominate during the `matter' and `radiation' eras respectively i.e. \Omega_m =1 when w_eff=0 and \Omega_r=1 when w_eff=1/3. We have found that the cosmological dynamical system constrained to obey the LCDM cosmic history has four critical points in each era which correspondingly lead to four forms of f(R). One of them is the usual general relativistic form f(R)=R-2\Lambda. The other three forms in each era, reproduce the LCDM cosmic history but they do not satisfy requirement b. stated above. Only one of these forms (different from general relativity) is found to be an attractor of the dynamical cosmological evolution. It has (\Omega_DE=1, \Omega_r=0, \Omega_m=0) throughout the evolution. Its phase space trajectory is numerically obtained.},
  creationdate     = {2022-01-24T19:36:59},
  doi              = {10.1103/physrevd.76.063504},
  eprint           = {0703006},
  file             = {:Fay2007.pdf:PDF},
  groups           = {f(R)},
  keywords         = {gr-qc},
  modificationdate = {2022-04-03T11:43:54},
}

@Article{Zhang2021,
  author           = {Yi Zhang and Hongsheng Zhang},
  journal          = {The European Physical Journal C},
  title            = {Distinguish the f(T) model from $\Lambda$CDM model with Gravitational Wave observations},
  year             = {2021},
  month            = {aug},
  number           = {8},
  volume           = {81},
  abstract         = {Separately, neither electromagnetic (EM) observations nor gravitational wave (GW) observations can distinguish between the $f(T)$ model and the $\Lambda$CDM model effectively. To break this degeneration, we simulate the GW measurement based on the coming observation facilities, explicitly the Einstein Telescope. We make crossvalidations between the simulated GW data and factual EM data, including the Pantheon, $H(z)$, BAO and CMBR data, and the results show that they are consistent with each other. Anyway, the EM data itself have the H₀ tension problem which plays critical role in the distinguishable problem as we will see. Our results show that the GW+BAO+CMBR data could distinguish the $f(T)$ theory from the $\Lambda$CDM model in 2$\sigma$ regime},
  comment          = {Consideram dois modelos baseados em f(T) onde apenas existe matéria, constante cosmologica é substituida por uma função de T. Os modelos são: 
- f<sub>p</sub>CDM, onde f(T) = T + α(-T)<sup>b</sup>
- f<sub>e</sub>CDM, onde f(T) = T + αT<sub>0</sub>(1 - e<sup>-p(T/T₀)<sup>1/2</sup></sup>)
Depois geram um catálogo para cada modelo, com os parâmetros constrangidos utilizado EM data e depois geram as GWs com esses valores.},
  creationdate     = {2022-01-24T23:02:57},
  doi              = {10.1140/epjc/s10052-021-09501-1},
  file             = {:Zhang2021.pdf:PDF},
  groups           = {Standard Sirens, f(T)},
  modificationdate = {2022-02-08T15:03:44},
  priority         = {prio1},
  publisher        = {Springer Science and Business Media {LLC}},
  readstatus       = {read},
}

@Article{Nesseris2013,
  author           = {S. Nesseris and S. Basilakos and E. N. Saridakis and L. Perivolaropoulos},
  journal          = {Phys. Rev. D 88, 103010 (2013)},
  title            = {Viable f(T) models are practically indistinguishable from LCDM},
  year             = {2013},
  month            = aug,
  abstract         = {We investigate the cosmological predictions of several $f(T)$ models, with up to two parameters, at both the background and the perturbation levels. Using current cosmological observations (geometric supernovae type Ia, cosmic microwave background and baryonic acoustic oscillation and dynamical growth data) we impose constraints on the distortion parameter, which quantifies the deviation of these models from the concordance $\Lambda$ cosmology at the background level. In addition we constrain the growth index $\gamma$ predicted in the context of these models using the latest perturbation growth data in the context of three parametrizations for $\gamma$. The evolution of the best fit effective Newton constant, which incorporates the $f(T)$-gravity effects, is also obtained along with the corresponding $1\sigma$ error regions. We show that all the viable parameter sectors of the $f(T)$ gravity models considered practically reduce these models to $\Lambda$CDM. Thus, the degrees of freedom that open up to $\Lambda$CDM in the context of $f(T)$ gravity models are not utilized by the cosmological data leading to an overall disfavor of these models.},
  archiveprefix    = {arXiv},
  comment          = {Considera vários modelos de f(T) e que apenas existe matéria e radiação.},
  creationdate     = {2022-01-24T23:13:12},
  doi              = {10.1103/PhysRevD.88.103010},
  eprint           = {1308.6142},
  file             = {:Nesseris2013.pdf:PDF},
  groups           = {f(T)},
  keywords         = {astro-ph.CO, gr-qc, hep-th},
  modificationdate = {2022-02-08T15:03:44},
  primaryclass     = {astro-ph.CO},
  priority         = {prio1},
}

@Article{Setare2013,
  author           = {M. R. Setare and N. Mohammadipour},
  journal          = {JCAP01(2013)015, doi:10.1088/1475-7516/2013/01/015},
  title            = {Can $f(T)$ gravity theories mimic $Λ$CDM cosmic history},
  year             = {2013},
  month            = jan,
  abstract         = {Recently the teleparallel Lagrangian density described by the torsion scalar T has been extended to a function of T. The $f(T)$ modified teleparallel gravity has been proposed as the natural gravitational alternative for dark energy to explain the late time acceleration of the universe. In order to reconstruct the function $f(T)$ by demanding a background $\Lambda$CDM cosmology we assume that, (i) the background cosmic history provided by the flat $\Lambda$CDM (the radiation ere with $\omega_{eff}=1/3$, matter and de Sitter eras with $\omega_{eff}=0$ and $\omega_{eff}=-1$, respectively) (ii) the radiation dominate in the radiation era with $\Omega_{0r}=1$ and the matter dominate during the matter phases when $\Omega_{0m}=1$. We find the cosmological dynamical system which can obey the $\Lambda$CDM cosmic history. In each era, we find a critical lines that, the radiation dominated and the matter dominated are one points of them in the radiation and matter phases, respectively. Also, we drive the cosmologically viability condition for these models. We investigate the stability condition with respect to the homogeneous scalar perturbations in each era and we obtain the stability conditions for the fixed points in each eras. Finally, we reconstruct the function $f(T)$ which mimics cosmic expansion history.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-24T23:15:42},
  doi              = {10.1088/1475-7516/2013/01/015},
  eprint           = {1301.4891},
  file             = {:Setare2013.pdf:PDF},
  groups           = {f(T)},
  keywords         = {gr-qc},
  modificationdate = {2022-02-08T15:03:44},
  primaryclass     = {gr-qc},
  priority         = {prio3},
}

@Article{Cai2016,
  author           = {Rong-Gen Cai and Tao Yang},
  journal          = {Phys. Rev. D 95, 044024 (2017)},
  title            = {Estimating cosmological parameters by the simulated data of gravitational waves from the Einstein Telescope},
  year             = {2016},
  month            = aug,
  abstract         = {We investigate the constraint ability of the gravitational wave (GW) as the standard siren on the cosmological parameters by using the third-generation gravitational wave detector: the Einstein Telescope. We simulate the luminosity distances and redshift measurements from 100 to 1000 GW events. We use two different algorithms to constrain the cosmological parameters. For the Hubble constant $H_0$ and dark matter density parameter $\Omega_m$, we adopt the Markov chain Monte Carlo approach. We find that with about 500-600 GW events we can constrain the Hubble constant with an accuracy comparable to \textit{Planck} temperature data and \textit{Planck} lensing combined results, while for the dark matter density, GWs alone seem not able to provide the constraints as good as for the Hubble constant; the sensitivity of 1000 GW events is a little lower than that of \textit{Planck} data. It should require more than 1000 events to match the \textit{Planck} sensitivity. Yet, for analyzing the more complex dynamical property of dark energy, i.e., the equation of state $w$, we adopt a new powerful nonparametric method: the Gaussian process. We can reconstruct $w$ directly from the observational luminosity distance at every redshift. In the low redshift region, we find that about 700 GW events can give the constraints of $w(z)$ comparable to the constraints of a constant $w$ by \textit{Planck} data with type Ia supernovae. Those results show that GWs as the standard sirens to probe the cosmological parameters can provide an independent and complementary alternative to current experiments.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-25T16:53:19},
  doi              = {10.1103/PhysRevD.95.044024},
  eprint           = {1608.08008},
  file             = {:Cai2016.pdf:PDF},
  groups           = {Standard Sirens},
  keywords         = {astro-ph.CO, gr-qc, hep-ph, hep-th},
  modificationdate = {2022-01-25T16:53:53},
  primaryclass     = {astro-ph.CO},
  priority         = {prio2},
}

@Article{Nunes2019,
  author           = {Rafael C. Nunes and Marcio E. S. Alves and Jose C. N. de Araujo},
  journal          = {Phys. Rev. D 100, 064012 (2019)},
  title            = {Forecast constraints on $f(T)$ gravity with gravitational waves from compact binary coalescences},
  year             = {2019},
  month            = may,
  abstract         = {The direct detection of gravitational waves (GWs) opened a new chapter in the modern cosmology to probe possible deviations from the general relativity (GR) theory. In the present work, we investigate for the first time the modified GW form propagation from the inspiraling of compact binary systems within the context of $f(T)$ gravity in order to obtain new forecasts/constraints on the free parameter of the theory. First, we show that the modified waveform differs from the GR waveform essentially due to induced corrections on the GWs amplitude. Then, we discuss the forecasts on the $f(T)$ gravity assuming simulated sources of GWs as black hole binaries, neutron star binaries and black hole - neutron star binary systems, which emit GWs in the frequency band of the Advanced LIGO (aLIGO) interferometer and of the third generation Einstein Telescope (ET). We show that GWs sources detected within the aLIGO sensitivity can return estimates of the same order of magnitude of the current cosmological observations. On the other hand, detection within the ET sensitivity can improve by up to 2 orders of magnitude the current bound on the $f(T)$ gravity. Therefore, the statistical accuracy that can be achieved by future ground based GW observations, mainly with the ET detector (and planed detectors with a similar sensitivity), can allow strong bounds on the free parameter of the theory, and can be decisive to test the theory of gravitation.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-01-26T10:29:03},
  doi              = {10.1103/PhysRevD.100.064012},
  eprint           = {1905.03237},
  file             = {:Nunes2019.pdf:PDF},
  groups           = {Standard Sirens, f(T)},
  keywords         = {gr-qc, astro-ph.CO, hep-ph},
  modificationdate = {2022-02-08T15:03:44},
  primaryclass     = {gr-qc},
  priority         = {prio1},
}

@Article{Boehmer2021,
  author           = {Christian G. Böhmer and Erik Jensko},
  journal          = {Physical Review D},
  title            = {Modified gravity: A unified approach},
  year             = {2021},
  month            = {jul},
  number           = {2},
  pages            = {024010},
  volume           = {104},
  abstract         = {Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in other popular modified gravity models. Using a more general setting the theory gives fourth order equations. This model is based on the metric alone and does not require more general geometries. It is possible to show that our new theory and the recently proposed f(Q) gravity models are equivalent at the level of the action and at the level of the field equations, provided that appropriate boundary terms are taken into account. Our theory can also reproduce f(R) gravity, which is an expected result. Perhaps more surprisingly, we show that this equivalence extends to f(T) gravity at the level of the action and its field equations, provided that appropriate boundary terms are taken in account. While these three theories are conceptually different and are based on different geometrical settings, we can establish the necessary conditions under which their field equations are the same. The final part requires matter to couple minimally to gravity. Through this work we emphasize the importance played by boundary terms which are at the heart of our approach.},
  creationdate     = {2022-02-08T14:58:16},
  doi              = {10.1103/physrevd.104.024010},
  file             = {:Boehmer2021.pdf:PDF},
  modificationdate = {2022-02-08T15:01:56},
  priority         = {prio2},
  publisher        = {American Physical Society ({APS})},
}

@Article{Ayuso2021,
  author           = {Ayuso, Ismael and Lazkoz, Ruth and Mimoso, Jos\'e Pedro},
  title            = {DGP and DGPish cosmologies from f(Q) actions},
  year             = {2021},
  month            = {11},
  archiveprefix    = {arXiv},
  creationdate     = {2022-03-22T13:50:26},
  eprint           = {2111.05061},
  file             = {:Ayuso2021.pdf:PDF},
  groups           = {f(Q)},
  modificationdate = {2022-03-22T13:51:05},
  primaryclass     = {astro-ph.CO},
  priority         = {prio3},
}

@Article{Albuquerque2022,
  author           = {In{\^{e}}s S. Albuquerque and Noemi Frusciante},
  journal          = {Physics of the Dark Universe},
  title            = {A designer approach to f(Q) gravity and cosmological implications},
  year             = {2022},
  month            = {mar},
  pages            = {100980},
  volume           = {35},
  archiveprefix    = {arXiv},
  creationdate     = {2022-03-23T23:17:18},
  doi              = {10.1016/j.dark.2022.100980},
  eprint           = {2202.04637},
  file             = {:Albuquerque2022.pdf:PDF},
  groups           = {f(Q)},
  modificationdate = {2022-03-23T23:18:35},
  primaryclass     = {astro-ph.CO},
  publisher        = {Elsevier {BV}},
}

@Article{Mandal2020,
  author           = {Mandal, Sanjay and Wang, Deng and Sahoo, P. K.},
  journal          = {Physical Review D},
  title            = {Cosmography in f(Q) gravity},
  year             = {2020},
  month            = {dec},
  number           = {12},
  pages            = {124029},
  volume           = {102},
  archiveprefix    = {arXiv},
  creationdate     = {2022-04-03T11:28:17},
  doi              = {10.1103/PhysRevD.102.124029},
  eprint           = {2011.00420},
  file             = {:Mandal2020.pdf:PDF},
  groups           = {f(Q)},
  modificationdate = {2022-04-03T11:30:10},
  primaryclass     = {gr-qc},
  publisher        = {American Physical Society ({APS})},
}

@Article{Lu2019,
  author           = {Jianbo Lu and Xin Zhao and Guoying Chee},
  journal          = {The European Physical Journal C},
  title            = {Cosmology in symmetric teleparallel gravity and its dynamical system},
  year             = {2019},
  month            = {jun},
  number           = {6},
  pages            = {530},
  volume           = {79},
  archiveprefix    = {arXiv},
  creationdate     = {2022-04-24T00:32:06},
  doi              = {10.1140/epjc/s10052-019-7038-3},
  eprint           = {1906.08920},
  file             = {:Lu2019.pdf:PDF},
  groups           = {f(Q), Dynamical Systems},
  modificationdate = {2022-04-26T12:27:55},
  primaryclass     = {gr-qc},
  publisher        = {Springer Science and Business Media {LLC}},
}

@InProceedings{Boehmer2014,
  author           = {Boehmer, Christian G. and Chan, Nyein},
  title            = {Dynamical systems in cosmology},
  year             = {2014},
  month            = {9},
  archiveprefix    = {arXiv},
  creationdate     = {2022-04-26T12:24:52},
  doi              = {10.1142/9781786341044_0004},
  eprint           = {1409.5585},
  file             = {:Boehmer2014.pdf:PDF},
  groups           = {Dynamical Systems},
  modificationdate = {2022-04-26T12:27:06},
  primaryclass     = {gr-qc},
  priority         = {prio2},
}

@Article{Hogg2020,
  author           = {N.B. Hogg and M. Martinelli and S. Nesseris},
  journal          = {Journal of Cosmology and Astroparticle Physics},
  title            = {Constraints on the distance duality relation with standard sirens},
  year             = {2020},
  month            = {dec},
  number           = {12},
  pages            = {019--019},
  volume           = {2020},
  abstract         = {We use gravitational wave (GW) standard sirens, in addition to Type Ia supernovae (SNIa) and baryon acoustic oscillation (BAO) mock data, to forecast constraints on the electromagnetic and gravitational distance duality relations (DDR). We make use of a parameterised approach based on a specific DDR violation model, along with a machine learning reconstruction method based on the Genetic Algorithms. We find that GW provide an alternative to the use of BAO data to constrain violations of the DDR, reaching $3\%$ constraints on the violation parameter we consider when combined with SNIa, which is only improved by a factor of $\approx1.4$ if one instead considers the combination of BAO and SNIa. We also investigate the possibility that a neglected modification of gravity might lead to a false detection of DDR violations, even when screening mechanisms are active. We find that such a false detection can be extremely significant, up to $\approx10\sigma$ for very extreme modified gravity scenarios, while this reduces to $\approx4\sigma$ in a more realistic case. False detections can also provide a smoking gun for the modified gravity mechanism at play, as a result of the tension introduced between the SNIa+GW and SNIa+BAO combinations.},
  archiveprefix    = {arXiv},
  creationdate     = {2022-05-24T11:18:59},
  doi              = {10.1088/1475-7516/2020/12/019},
  eprint           = {2007.14335},
  file             = {:Hogg2020.pdf:PDF},
  groups           = {SNIa, Standard Sirens, BAO},
  keywords         = {astro-ph.CO},
  modificationdate = {2022-05-24T11:20:35},
  primaryclass     = {astro-ph.CO},
  priority         = {prio2},
  publisher        = {{IOP} Publishing},
}

@Article{Astier2014,
  author           = {P. Astier and C. Balland and M. Brescia and E. Cappellaro and R. G. Carlberg and S. Cavuoti and M. Della Valle and E. Gangler and A. Goobar and J. Guy and D. Hardin and I. M. Hook and R. Kessler and A. Kim and E. Linder and G. Longo and K. Maguire and F. Mannucci and S. Mattila and R. Nichol and R. Pain and N. Regnault and S. Spiro and M. Sullivan and C. Tao and M. Turatto and X. F. Wang and W. M. Wood-Vasey},
  journal          = {Astronomy {\&}amp$\mathsemicolon$ Astrophysics},
  title            = {Extending the supernova Hubble diagram to z~1.5 with the Euclid space mission},
  year             = {2014},
  month            = {dec},
  pages            = {A80},
  volume           = {572},
  abstract         = {We forecast dark energy constraints that could be obtained from a new large sample of Type Ia supernovae where those at high redshift are acquired with the Euclid space mission. We simulate a three-prong SN survey: a z<0.35 nearby sample (8000 SNe), a 0.2<z<0.95 intermediate sample (8800 SNe), and a 0.75<z<1.55 high-z sample (1700 SNe). The nearby and intermediate surveys are assumed to be conducted from the ground, while the high-z is a joint ground- and space-based survey. This latter survey, the "Dark Energy Supernova Infra-Red Experiment" (DESIRE), is designed to fit within 6 months of Euclid observing time, with a dedicated observing program. We simulate the SN events as they would be observed in rolling-search mode by the various instruments, and derive the quality of expected cosmological constraints. We account for known systematic uncertainties, in particular calibration uncertainties including their contribution through the training of the supernova model used to fit the supernovae light curves. Using conservative assumptions and a 1-D geometric Planck prior, we find that the ensemble of surveys would yield competitive constraints: a constant equation of state parameter can be constrained to sigma(w)=0.022, and a Dark Energy Task Force figure of merit of 203 is found for a two-parameter equation of state. Our simulations thus indicate that Euclid can bring a significant contribution to a purely geometrical cosmology constraint by extending a high-quality SN Hubble diagram to z~1.5. We also present other science topics enabled by the DESIRE Euclid observations},
  archiveprefix    = {arXiv},
  creationdate     = {2022-05-25T10:16:45},
  doi              = {10.1051/0004-6361/201423551},
  eprint           = {1409.8562},
  file             = {:Astier2014.pdf:PDF},
  groups           = {SNIa},
  keywords         = {astro-ph.CO},
  modificationdate = {2022-05-25T10:17:27},
  primaryclass     = {astro-ph.CO},
  publisher        = {{EDP} Sciences},
}

@Article{Anagnostopoulos2018,
  author           = {Fotios K. Anagnostopoulos and Spyros Basilakos},
  journal          = {Physical Review D},
  title            = {Constraining the dark energy models with H(z) data: An approach independent of H_0},
  year             = {2018},
  month            = {mar},
  number           = {6},
  pages            = {063503},
  volume           = {97},
  archiveprefix    = {arXiv},
  creationdate     = {2022-06-02T10:10:57},
  doi              = {10.1103/physrevd.97.063503},
  eprint           = {1709.02356},
  file             = {:Anagnostopoulos2018.pdf:PDF},
  modificationdate = {2022-06-02T10:11:52},
  primaryclass     = {astro-ph.CO},
  publisher        = {American Physical Society ({APS})},
}

@Article{advLIGO,
  author           = {The LIGO Scientific Collaboration},
  journal          = {Classical and Quantum Gravity},
  title            = {Advanced {LIGO}},
  year             = {2015},
  month            = {mar},
  number           = {7},
  pages            = {074001},
  volume           = {32},
  doi              = {10.1088/0264-9381/32/7/074001},
  modificationdate = {2022-06-29T10:28:01},
  publisher        = {{IOP} Publishing},
}

@Article{advVirgo,
  author           = {The Virgo Collaboration},
  journal          = {Classical and Quantum Gravity},
  title            = {Advanced Virgo: a second-generation interferometric gravitational wave detector},
  year             = {2014},
  month            = {dec},
  number           = {2},
  pages            = {024001},
  volume           = {32},
  doi              = {10.1088/0264-9381/32/2/024001},
  modificationdate = {2022-06-29T10:30:18},
  publisher        = {{IOP} Publishing},
}

@Article{Vehtari2021,
  author           = {Aki Vehtari and Andrew Gelman and Daniel Simpson and Bob Carpenter and Paul-Christian Bürkner},
  journal          = {Bayesian Analysis},
  title            = {Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of {MCMC} (with Discussion)},
  year             = {2021},
  month            = {jun},
  number           = {2},
  volume           = {16},
  creationdate     = {2022-06-29T15:06:35},
  doi              = {10.1214/20-ba1221},
  modificationdate = {2022-06-29T15:06:35},
  publisher        = {Institute of Mathematical Statistics},
}

@Article{Anagnostopoulos2022,
  author           = {Anagnostopoulos, Fotios K. and Gakis, Viktor and Saridakis, Emmanuel N. and Basilakos, Spyros},
  title            = {New models and Big Bang Nucleosynthesis constraints in f(Q) gravity},
  year             = {2022},
  month            = {5},
  archiveprefix    = {arXiv},
  creationdate     = {2022-07-01T12:00:57},
  eprint           = {2205.11445},
  groups           = {f(Q)},
  modificationdate = {2022-07-01T12:00:57},
  primaryclass     = {gr-qc},
}

@Article{Ferreira2022,
  author           = {Ferreira, Jos\'e and Barreiro, Tiago and Mimoso, Jos\'e and Nunes, Nelson J.},
  journal          = {Phys. Rev. D},
  title            = {Forecasting F(Q) cosmology with \ensuremath{Λ}{C}{D}M background using standard sirens},
  year             = {2022},
  number           = {12},
  pages            = {123531},
  volume           = {105},
  archiveprefix    = {arXiv},
  creationdate     = {2022-08-02T15:40:33},
  doi              = {10.1103/PhysRevD.105.123531},
  eprint           = {2203.13788},
  groups           = {f(Q), Standard Sirens},
  modificationdate = {2022-08-02T15:40:47},
  primaryclass     = {astro-ph.CO},
}

@Article{Carroll2001,
  author           = {Sean M. Carroll},
  journal          = {Living Reviews in Relativity},
  title            = {The Cosmological Constant},
  year             = {2001},
  month            = {feb},
  number           = {1},
  volume           = {4},
  creationdate     = {2022-08-10T11:51:40},
  doi              = {10.12942/lrr-2001-1},
  file             = {:Carroll2001.pdf:PDF},
  groups           = {Review},
  modificationdate = {2022-08-10T11:52:13},
  publisher        = {Springer Science and Business Media {LLC}},
}

@Article{Vehtari2015,
  author           = {Aki Vehtari and Andrew Gelman and Jonah Gabry},
  journal          = {Statistics and Computing},
  title            = {Practical Bayesian model evaluation using leave-one-out cross-validation and {WAIC}},
  year             = {2016},
  month            = {aug},
  number           = {5},
  pages            = {1413--1432},
  volume           = {27},
  archiveprefix    = {arXiv},
  creationdate     = {2022-08-11T12:36:54},
  doi              = {10.1007/s11222-016-9696-4},
  eprint           = {1507.04544},
  file             = {:Vehtari2015.pdf:PDF},
  groups           = {Statistics},
  keywords         = {stat.CO, stat.ME},
  modificationdate = {2022-08-11T12:45:56},
  primaryclass     = {stat.CO},
  publisher        = {Springer Science and Business Media {LLC}},
}

@Article{Gelman2013,
  author           = {Andrew Gelman and Jessica Hwang and Aki Vehtari},
  title            = {Understanding predictive information criteria for Bayesian models},
  year             = {2013},
  month            = jul,
  archiveprefix    = {arXiv},
  creationdate     = {2022-08-11T15:29:42},
  eprint           = {1307.5928},
  file             = {:Gelman2013.pdf:PDF},
  groups           = {Statistics},
  keywords         = {stat.ME},
  modificationdate = {2022-08-11T15:29:45},
  primaryclass     = {stat.ME},
}

@Article{arviz,
  author           = {Ravin Kumar and Colin Carroll and Ari Hartikainen and Osvaldo Martin},
  journal          = {Journal of Open Source Software},
  title            = {{ArviZ} a unified library for exploratory analysis of Bayesian models in Python},
  year             = {2019},
  month            = {jan},
  number           = {33},
  pages            = {1143},
  volume           = {4},
  doi              = {10.21105/joss.01143},
  groups           = {Software},
  modificationdate = {2022-08-16T23:30:11},
  publisher        = {The Open Journal},
  url              = {https://doi.org/10.21105/joss.01143},
}

@Book{Bergmann1976,
  author           = {Bergmann, Peter Gabriel},
  title            = {Introduction to the theory of relativity},
  isbn             = {0486632822},
  pages            = {307},
  publisher        = {Dover Publications},
  creationdate     = {2022-08-24T11:21:37},
  file             = {:Bergmann1976.pdf:PDF},
  modificationdate = {2022-08-24T11:22:25},
  year             = {1976},
}

@Book{Tonnelat2014,
  author           = {Tonnelat, Marie-Antoinette},
  title            = {Einstein's Theory of Unified Fields},
  isbn             = {9781138013629},
  pages            = {200},
  publisher        = {Taylor \& Francis Group},
  creationdate     = {2022-08-24T11:48:09},
  file             = {:Tonnelat2014.pdf:PDF},
  modificationdate = {2022-08-24T11:48:38},
  year             = {2014},
}

@Book{Strogatz,
  author           = {Strogatz, Steven H.},
  title            = {Nonlinear Dynamics and Chaos with Student Solutions Manual: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and ... Edition (Studies in Nonlinearity) (Volume 1)},
  isbn             = {9780813349107},
  pages            = {531},
  publisher        = {Westview Press},
  subtitle         = {With Applications to Physics, Biology, Chemistry, and Engineering},
  creationdate     = {2022-09-08T14:19:11},
  groups           = {Books},
  modificationdate = {2022-09-08T14:19:11},
}

@Article{Jaerv2018,
  author           = {Laur Järv and Mihkel Rünkla and Margus Saal and Ott Vilson},
  date             = {2018-02-01},
  journaltitle     = {Phys. Rev. D 97, 124025 (2018)},
  title            = {Nonmetricity formulation of general relativity and its scalar-tensor extension},
  doi              = {10.1103/PhysRevD.97.124025},
  eprint           = {1802.00492},
  eprintclass      = {gr-qc},
  eprinttype       = {arXiv},
  abstract         = {Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of theories where a scalar field is coupled nonminimally to nonmetricity $Q$, which here encodes the gravitational effects like curvature $R$ in general relativity or torsion $T$ in teleparallel gravity. We point out the similarities and differences with analogous scalar-curvature and scalar-torsion theories by discussing the field equations, role of connection, conformal transformations, relation to $f(Q)$ theory, and cosmology. The equations for spatially flat universe coincide with those of teleparallel dark energy, thus allowing to explain accelerating expansion.},
  creationdate     = {2022-09-10T11:57:03},
  file             = {:Jaerv2018.pdf:PDF},
  groups           = {f(Q)},
  keywords         = {gr-qc, hep-ph, hep-th, 83D05},
  modificationdate = {2022-09-10T11:57:08},
}

@Book{Amendola2010,
  author           = {Amendola, Luca},
  date             = {2010},
  title            = {Dark energy},
  isbn             = {9780521516006},
  publisher        = {Cambridge University Press},
  subtitle         = {theory and observations},
  creationdate     = {2022-09-11T19:54:35},
  groups           = {Books},
  modificationdate = {2022-09-11T19:54:35},
}

@Article{Koivisto2005,
  author           = {Koivisto, Tomi},
  date             = {2005},
  title            = {Covariant conservation of energy momentum in modified gravities},
  doi              = {10.48550/ARXIV.GR-QC/0505128},
  copyright        = {Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004},
  creationdate     = {2022-09-12T11:11:15},
  keywords         = {General Relativity and Quantum Cosmology (gr-qc), FOS: Physical sciences, FOS: Physical sciences},
  modificationdate = {2022-09-12T11:11:15},
  publisher        = {arXiv},
}

@Book{Faraoni2011,
  author           = {Faraoni, Valerio},
  date             = {2011},
  title            = {Beyond Einstein Gravity},
  isbn             = {9789400701649},
  publisher        = {Springer Science+Business Media B.V.},
  subtitle         = {A Survey of Gravitational Theories for Cosmology and Astrophysics},
  creationdate     = {2022-09-12T11:32:09},
  groups           = {Books},
  modificationdate = {2022-09-12T11:32:09},
}

@Book{Maggiore2018,
  author           = {Maggiore, Michele},
  title            = {Gravitational Waves : Volume 2 Astrophysics and Cosmology},
  isbn             = {9780198570899},
  publisher        = {Oxford University Press},
  subtitle         = {Astrophysics and Cosmology},
  creationdate     = {2022-09-20T15:07:12},
  groups           = {Books},
  modificationdate = {2022-09-20T15:12:33},
  year             = {2018},
}

@Book{Maggiore2007,
  author           = {Maggiore, Michele},
  date             = {2007},
  title            = {Gravitational Waves: Volume 1: Theory and Experiments Volume 1},
  isbn             = {9780198570745},
  pages            = {288},
  publisher        = {Oxford University Press, USA},
  subtitle         = {Theory and Experiments},
  creationdate     = {2022-09-20T15:09:04},
  groups           = {Books},
  modificationdate = {2022-09-20T15:09:06},
}

@Article{Antonini2015,
  author           = {Fabio Antonini and Enrico Barausse and Joseph Silk},
  date             = {2015-06-05},
  journaltitle     = {The Astrophysical Journal},
  title            = {Co-evolution of nuclear star clusters, massive black holes and their host galaxies},
  doi              = {10.1088/0004-637x/812/1/72},
  eprint           = {1506.02050},
  eprintclass      = {astro-ph.GA},
  eprinttype       = {arXiv},
  number           = {1},
  pages            = {72},
  volume           = {812},
  keywords         = {astro-ph.GA, astro-ph.CO, gr-qc},
  publisher        = {American Astronomical Society},
}

@Article{Felice2010,
  author           = {Antonio De Felice and Shinji Tsujikawa},
  date             = {2010-02-26},
  journaltitle     = {Living Reviews in Relativity},
  title            = {f(R) Theories},
  doi              = {10.12942/lrr-2010-3},
  eprint           = {1002.4928},
  eprintclass      = {gr-qc},
  eprinttype       = {arXiv},
  number           = {1},
  volume           = {13},
  keywords         = {gr-qc, astro-ph.CO, hep-ph, hep-th},
  publisher        = {Springer Science and Business Media {LLC}},
}

@misc{Zwicky1933,
  doi = {10.48550/ARXIV.1711.01693},
  url = {https://arxiv.org/abs/1711.01693},
  author = {Andernach, Heinz and Zwicky, Fritz},
  keywords = {Instrumentation and Methods for Astrophysics (astro-ph.IM), Astrophysics of Galaxies (astro-ph.GA), FOS: Physical sciences, FOS: Physical sciences},
  title = {English and Spanish Translation of Zwicky's (1933) The Redshift of Extragalactic Nebulae},
  publisher = {arXiv},
  year = {2017},
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@article{SupernovaCosmologyProject1998,
    author = "Perlmutter, S. and others",
    collaboration = "Supernova Cosmology Project",
    title = "{Measurements of $\Omega$ and $\Lambda$ from 42 high redshift supernovae}",
    eprint = "astro-ph/9812133",
    archivePrefix = "arXiv",
    reportNumber = "LBNL-41801, LBL-41801",
    doi = "10.1086/307221",
    journal = "Astrophys. J.",
    volume = "517",
    pages = "565--586",
    year = "1999"
}