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The Next Generation Global Gravitational Wave Observatory: The Science Book
Authors:
Vicky Kalogera,
B. S. Sathyaprakash,
Matthew Bailes,
Marie-Anne Bizouard,
Alessandra Buonanno,
Adam Burrows,
Monica Colpi,
Matt Evans,
Stephen Fairhurst,
Stefan Hild,
Mansi M. Kasliwal,
Luis Lehner,
Ilya Mandel,
Vuk Mandic,
Samaya Nissanke,
Maria Alessandra Papa,
Sanjay Reddy,
Stephan Rosswog,
Chris Van Den Broeck,
P. Ajith,
Shreya Anand,
Igor Andreoni,
K. G. Arun,
Enrico Barausse,
Masha Baryakhtar
, et al. (66 additional authors not shown)
Abstract:
The next generation of ground-based gravitational-wave detectors will observe coalescences of black holes and neutron stars throughout the cosmos, thousands of them with exceptional fidelity. The Science Book is the result of a 3-year effort to study the science capabilities of networks of next generation detectors. Such networks would make it possible to address unsolved problems in numerous area…
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The next generation of ground-based gravitational-wave detectors will observe coalescences of black holes and neutron stars throughout the cosmos, thousands of them with exceptional fidelity. The Science Book is the result of a 3-year effort to study the science capabilities of networks of next generation detectors. Such networks would make it possible to address unsolved problems in numerous areas of physics and astronomy, from Cosmology to Beyond the Standard Model of particle physics, and how they could provide insights into workings of strongly gravitating systems, astrophysics of compact objects and the nature of dense matter. It is inevitable that observatories of such depth and finesse will make new discoveries inaccessible to other windows of observation. In addition to laying out the rich science potential of the next generation of detectors, this report provides specific science targets in five different areas in physics and astronomy and the sensitivity requirements to accomplish those science goals.
This report is the second in a six part series of reports by the GWIC 3G Subcommittee: i) Expanding the Reach of Gravitational Wave Observatories to the Edge of the Universe, ii) The Next Generation Global Gravitational Wave Observatory: The Science Book (this report), iii) 3G R&D: R&D for the Next Generation of Ground-based Gravitational Wave Detectors, iv) Gravitational Wave Data Analysis: Computing Challenges in the 3G Era, v) Future Ground-based Gravitational-wave Observatories: Synergies with Other Scientific Communities, and vi) An Exploration of Possible Governance Models for the Future Global Gravitational-Wave Observatory Network.
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Submitted 12 November, 2021;
originally announced November 2021.
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Gravity in the infrared and effective nonlocal models
Authors:
Enis Belgacem,
Yves Dirian,
Andreas Finke,
Stefano Foffa,
Michele Maggiore
Abstract:
We provide a systematic and updated discussion of a research line carried out by our group over the last few years, in which gravity is modified at cosmological distances by the introduction of nonlocal terms, assumed to emerge at an effective level from the infrared behavior of the quantum theory. The requirement of producing a viable cosmology turns out to be very stringent and basically selects…
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We provide a systematic and updated discussion of a research line carried out by our group over the last few years, in which gravity is modified at cosmological distances by the introduction of nonlocal terms, assumed to emerge at an effective level from the infrared behavior of the quantum theory. The requirement of producing a viable cosmology turns out to be very stringent and basically selects a unique model, in which the nonlocal term describes an effective mass for the conformal mode. We discuss how such a specific structure could emerge from a fundamental local theory of gravity, and we perform a detailed comparison of this model with the most recent cosmological datasets, confirming that it fits current data at the same level as $Λ$CDM.
Most notably, the model has striking predictions in the sector of tensor perturbations, leading to a very large effect in the propagation of gravitational wave (GWs) over cosmological distances. At the redshifts relevant for the next generation of GW detectors such as Einstein Telescope, Cosmic Explorer and LISA, this leads to deviations from GR that could be as large as $80\%$, and could be verified with the detection of just a single coalescing binary with electromagnetic counterpart. This would also have potentially important consequences for the search of the counterpart since, for a given luminosity distance to the source, as inferred through the GW signal, the actual source redshift could be significantly different from that predicted by $Λ$CDM. At the redshifts relevant for advanced LIGO/Virgo/Kagra the effect is smaller, but still potentially observable over a few years of runs at target sensitivity.
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Submitted 21 January, 2020;
originally announced January 2020.
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Testing modified gravity at cosmological distances with LISA standard sirens
Authors:
E. Belgacem,
G. Calcagni,
M. Crisostomi,
C. Dalang,
Y. Dirian,
J. M. Ezquiaga,
M. Fasiello,
S. Foffa,
A. Ganz,
J. Garcia-Bellido,
L. Lombriser,
M. Maggiore,
N. Tamanini,
G. Tasinato,
M. Zumalacarregui,
E. Barausse,
N. Bartolo,
D. Bertacca,
A. Klein,
S. Matarrese,
M. Sakellariadou
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 electromag…
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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 $(Ξ_0,n)$, 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 $Ξ_0$ that characterizes modified GW propagation to the percent level accuracy, sufficient to test several modified gravity theories. [Abridged]
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Submitted 4 July, 2019; v1 submitted 4 June, 2019;
originally announced June 2019.
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General Relativistic Cosmological N-body Simulations I: time integration
Authors:
David Daverio,
Yves Dirian,
Ermis Mitsou
Abstract:
This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization method and time-integration algorithm that provides satisfyingly stable evolution. More precisely, we show that it is able to pass a robustness test and to follow s…
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This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization method and time-integration algorithm that provides satisfyingly stable evolution. More precisely, we show that it is able to pass a robustness test and to follow scalar linear modes around an expanding homogeneous and isotropic space-time. Most importantly, it is able to evolve typical cosmological initial conditions on comoving scales down to tenths of megaparsecs with controlled constraint and energy-momentum conservation violations all the way down to the regime of strong inhomogeneity.
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Submitted 28 October, 2019; v1 submitted 16 April, 2019;
originally announced April 2019.
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Cosmology and the Early Universe
Authors:
B. S. Sathyaprakash,
Enis Belgacem,
Daniele Bertacca,
Chiara Caprini,
Giulia Cusin,
Yves Dirian,
Xilong Fan,
Daniel Figueroa,
Stefano Foffa,
Evan Hall,
Jan Harms,
Michele Maggiore,
Vuk Mandic,
Andrew Matas,
Tania Regimbau,
Mairi Sakellariadou,
Nicola Tamanini,
Eric Thrane
Abstract:
This Astro-2020 White Paper deals with what we might learn from future gravitational wave observations about the early universe phase transitions and their energy scales, primordial black holes, Hubble parameter, dark matter and dark energy, modified theories of gravity and extra dimensions.
This Astro-2020 White Paper deals with what we might learn from future gravitational wave observations about the early universe phase transitions and their energy scales, primordial black holes, Hubble parameter, dark matter and dark energy, modified theories of gravity and extra dimensions.
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Submitted 21 March, 2019;
originally announced March 2019.
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Observational Constraints in Nonlocal Gravity: the Deser-Woodard Case
Authors:
Luca Amendola,
Yves Dirian,
Henrik Nersisyan,
Sohyun Park
Abstract:
We study the cosmology of a specific class of nonlocal model of modified gravity, the so-called Deser-Woodard (DW) model, modifying the Einstein-Hilbert action by a term $\sim R f(\Box^{-1}R)$, where $f$ is a free function. Choosing $f$ so as to reproduce the $Λ{\rm CDM}$ cosmological background expansion history within the nonlocal model, we implement the model in a cosmological linear Einstein--…
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We study the cosmology of a specific class of nonlocal model of modified gravity, the so-called Deser-Woodard (DW) model, modifying the Einstein-Hilbert action by a term $\sim R f(\Box^{-1}R)$, where $f$ is a free function. Choosing $f$ so as to reproduce the $Λ{\rm CDM}$ cosmological background expansion history within the nonlocal model, we implement the model in a cosmological linear Einstein--Boltzmann solver and study the deviations to GR the model induces in the scalar and tensor perturbations. We observe that the DW nonlocal model describes a modified propagation for the gravitational waves, as well as a lower linear growth rate and a stronger lensing power as compared to $Λ{\rm CDM}$, up to several percents. Such prominent growth and lensing features lead to the inference of a significantly smaller value of $σ_8$ with respect to the one in $Λ{\rm CDM}$, given \textit{Planck} CMB+lensing data. The prediction for the linear growth rate $f σ_8$ within the DW model is therefore significantly smaller than the one in $Λ{\rm CDM}$ and the addition of growth rate data $f σ_8$ from Redshift-space distortion measurements to \textit{Planck} CMB+lensing, opens a (dominant) tension between Redshift-space distortion data and the reconstructed \textit{Planck} CMB lensing potential. However, model selection issues only result in "weak" evidences for $Λ{\rm CDM}$ against the DW model given the data. Such a fact shows that the datasets we consider are not constraining enough for distinguishing between the models. As we discuss, the addition of galaxy WL data or cosmological constraints from future galaxy clustering, weak lensing surveys, but also third generation gravitational wave interferometers, prove to be useful for discriminating modified gravity models such as the DW one from $Λ{\rm CDM}$, within the close future.
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Submitted 17 April, 2019; v1 submitted 23 January, 2019;
originally announced January 2019.
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Apples with Apples comparison of 3+1 conformal numerical relativity schemes
Authors:
David Daverio,
Yves Dirian,
Ermis Mitsou
Abstract:
This paper contains a comprehensive comparison catalog of `Apples with Apples' tests for the BSSNOK, CCZ4 and Z4c numerical relativity schemes, with and without constraint damping terms for the latter two. We use basic numerical methods and reach the same level of accuracy as existing results in the literature. We find that the best behaving scheme is generically CCZ4 with constraint damping terms…
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This paper contains a comprehensive comparison catalog of `Apples with Apples' tests for the BSSNOK, CCZ4 and Z4c numerical relativity schemes, with and without constraint damping terms for the latter two. We use basic numerical methods and reach the same level of accuracy as existing results in the literature. We find that the best behaving scheme is generically CCZ4 with constraint damping terms.
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Submitted 29 October, 2018;
originally announced October 2018.
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Modified gravitational-wave propagation and standard sirens
Authors:
Enis Belgacem,
Yves Dirian,
Stefano Foffa,
Michele Maggiore
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…
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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 $(Ξ_0,n)$, 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 $(Ξ_0,n)$, 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, $Ξ_0$ 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.
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Submitted 28 June, 2018; v1 submitted 22 May, 2018;
originally announced May 2018.
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The gravitational-wave luminosity distance in modified gravity theories
Authors:
Enis Belgacem,
Yves Dirian,
Stefano Foffa,
Michele Maggiore
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 $δ(z)$ describing modified propagation. We show that the effect of modified propagation in…
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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 $δ(z)$ 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 $Λ$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 $Λ$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.
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Submitted 15 May, 2018; v1 submitted 21 December, 2017;
originally announced December 2017.
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Nonlocal gravity. Conceptual aspects and cosmological predictions
Authors:
Enis Belgacem,
Yves Dirian,
Stefano Foffa,
Michele Maggiore
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, i…
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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 $Λ$ 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 $Λ$CDM. (4) Bayesian parameter estimation shows that the value of $H_0$ obtained in the RR model is higher than in $Λ$CDM, reducing to $2.0σ$ 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.
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Submitted 15 January, 2018; v1 submitted 19 December, 2017;
originally announced December 2017.
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Changing the prior: absolute neutrino mass constraints in nonlocal gravity
Authors:
Yves Dirian
Abstract:
Prior change is discussed in observational constraints studies of nonlocally modified gravity. In the latter, a model characterized by a modification of the form $\sim m^2 R\Box^{-2}R$ to the Einstein-Hilbert action was compared against the base $Λ$CDM one in a Bayesian way. It was found that the competing modified gravity model is significantly disfavored (at $22 \,$:$\, 1$ in terms of betting-od…
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Prior change is discussed in observational constraints studies of nonlocally modified gravity. In the latter, a model characterized by a modification of the form $\sim m^2 R\Box^{-2}R$ to the Einstein-Hilbert action was compared against the base $Λ$CDM one in a Bayesian way. It was found that the competing modified gravity model is significantly disfavored (at $22 \,$:$\, 1$ in terms of betting-odds) against $Λ$CDM given CMB+SNIa+BAO data, because of a dominant tension appearing in the $H_0 \,$-$\, Ω_M$ plan. We identify the underlying mechanism generating such a tension and show that it is mostly caused by the late-time, quite smooth, phantom nature of the effective dark energy described by the nonlocal model. We find possible solutions for it to be resolved and explore a given one that consists in extending the initial baseline from one massive neutrino eigenstate to three degenerate ones, whose absolute mass $\sum m_ν\, / \, 3$ is allowed to take values within a reasonable prior interval. As a net effect, the absolute neutrino mass is inferred to be non-vanishing at $2 σ$ level, best-fitting at $\sum m_ν\approx 0.21 {\, \rm eV}$, and the Bayesian tension disappears rendering the nonlocal gravity model statistically equivalent to $Λ$CDM, given recent CMB+SNIa+BAO data. We also discuss constraints from growth rate measurements $f σ_8$ whose fit is found to be improved by a larger massive neutrino fraction as well. The $ν$-extended nonlocal model also prefers a higher value of $H_0$ than $Λ$CDM, therefore in better agreement with local measurements.
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Submitted 5 October, 2017; v1 submitted 13 April, 2017;
originally announced April 2017.
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A numerical relativity scheme for cosmological simulations
Authors:
David Daverio,
Yves Dirian,
Ermis Mitsou
Abstract:
Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3+1 integration scheme for General Relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The origin…
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Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3+1 integration scheme for General Relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.
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Submitted 13 November, 2017; v1 submitted 10 November, 2016;
originally announced November 2016.
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Non-local gravity and comparison with observational datasets. II. Updated results and Bayesian model comparison with $Λ$CDM
Authors:
Yves Dirian,
Stefano Foffa,
Martin Kunz,
Michele Maggiore,
Valeria Pettorino
Abstract:
We present a comprehensive and updated comparison with cosmological observations of two non-local modifications of gravity previously introduced by our group, the so called RR and RT models. We implement the background evolution and the cosmological perturbations of the models in a modified Boltzmann code, using CLASS. We then test the non-local models against the {\em Planck} 2015 TT, TE, EE and…
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We present a comprehensive and updated comparison with cosmological observations of two non-local modifications of gravity previously introduced by our group, the so called RR and RT models. We implement the background evolution and the cosmological perturbations of the models in a modified Boltzmann code, using CLASS. We then test the non-local models against the {\em Planck} 2015 TT, TE, EE and Cosmic Microwave Background (CMB) lensing data, isotropic and anisotropic Baryonic Acoustic Oscillations (BAO) data, JLA supernovae, $H_0$ measurements and growth rate data, and we perform Bayesian parameter estimation. We then compare the RR, RT and $Λ$CDM models, using the Savage-Dickey method. We find that the RT model and $Λ$CDM perform equally well, while the performance of the RR model with respect to $Λ$CDM depends on whether or not we include a prior on $H_0$ based on local measurements.
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Submitted 22 May, 2016; v1 submitted 10 February, 2016;
originally announced February 2016.
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Non-local gravity and comparison with observational datasets
Authors:
Yves Dirian,
Stefano Foffa,
Martin Kunz,
Michele Maggiore,
Valeria Pettorino
Abstract:
We study the cosmological predictions of two recently proposed non-local modifications of General Relativity. Both models have the same number of parameters as $Λ$CDM, with a mass parameter $m$ replacing the cosmological constant. We implement the cosmological perturbations of the non-local models into a modification of the CLASS Boltzmann code, and we make a full comparison to CMB, BAO and supern…
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We study the cosmological predictions of two recently proposed non-local modifications of General Relativity. Both models have the same number of parameters as $Λ$CDM, with a mass parameter $m$ replacing the cosmological constant. We implement the cosmological perturbations of the non-local models into a modification of the CLASS Boltzmann code, and we make a full comparison to CMB, BAO and supernova data. We find that the non-local models fit these datasets as well as $Λ$CDM. For both non-local models parameter estimation using Planck+JLA+BAO data gives a value of $H_0$ higher than in $Λ$CDM, and in better agreement with the values obtained from local measurements.
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Submitted 27 November, 2014;
originally announced November 2014.
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Stability analysis and future singularity of the $m^2 R \Box^{-2} R$ model of non-local gravity
Authors:
Yves Dirian,
Ermis Mitsou
Abstract:
We analyse the classical stability of the model proposed by Maggiore and Mancarella, where gravity is modified by a term $\sim m^2 R \Box^{-2} R$ to produce the late-time acceleration of the expansion of the universe. Our study takes into account all excitations of the metric that can potentially drive an instability. There are some subtleties in identifying these modes, as a non-local field theor…
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We analyse the classical stability of the model proposed by Maggiore and Mancarella, where gravity is modified by a term $\sim m^2 R \Box^{-2} R$ to produce the late-time acceleration of the expansion of the universe. Our study takes into account all excitations of the metric that can potentially drive an instability. There are some subtleties in identifying these modes, as a non-local field theory contains dynamical fields which yet do not correspond to degrees of freedom. Since some of them are ghost-like, we clarify the impact of such modes on the stability of the solutions of interest that are the flat space-time and cosmological solutions. We then find that flat space-time is unstable under scalar perturbations, but the instability manifests itself only at cosmological scales, i.e. out of the region of validity of this solution. It is therefore the stability of the FLRW solution which is relevant there, in which case the scalar perturbations are known to be well-behaved by numerical studies. By finding the analytic solution for the late-time behaviour of the scale factor, which leads to a big rip singularity, we argue that the linear perturbations are bounded in the future because of the domination of Hubble friction. In particular, this effect damps the scalar ghost perturbations which were responsible for destabilizing Minkowski space-time. Thus, the model remains phenomenologically viable.
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Submitted 2 December, 2014; v1 submitted 21 August, 2014;
originally announced August 2014.
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Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity
Authors:
Yves Dirian,
Stefano Foffa,
Nima Khosravi,
Martin Kunz,
Michele Maggiore
Abstract:
We study the cosmological consequences of a recently proposed nonlocal modification of general relativity, obtained by adding a term $m^2R\,\Box^{-2}R$ to the Einstein-Hilbert action. The model has the same number of parameters as $Λ$CDM, with $m$ replacing $Ω_Λ$, and is very predictive. At the background level, after fixing $m$ so as to reproduce the observed value of $Ω_M$, we get a pure predict…
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We study the cosmological consequences of a recently proposed nonlocal modification of general relativity, obtained by adding a term $m^2R\,\Box^{-2}R$ to the Einstein-Hilbert action. The model has the same number of parameters as $Λ$CDM, with $m$ replacing $Ω_Λ$, and is very predictive. At the background level, after fixing $m$ so as to reproduce the observed value of $Ω_M$, we get a pure prediction for the equation of state of dark energy as a function of redshift, $w_{\rm DE}(z)$, with $w_{\rm DE}(0)$ in the range $[-1.165,-1.135]$ as $Ω_M$ varies over the broad range $Ω_M\in [0.20,0.36]$. We find that the cosmological perturbations are well-behaved, and the model fully fixes the dark energy perturbations as a function of redshift $z$ and wavenumber $k$. The nonlocal model provides a good fit to supernova data and predicts deviations from General Relativity in structure formation and in weak lensing at the level of 3-4%, therefore consistent with existing data but readily detectable by future surveys. For the logarithmic growth factor we obtain $γ\simeq 0.53$, to be compared with $γ\simeq 0.55$ in $Λ$CDM. For the Newtonian potential on subhorizon scales our results are well fitted by $Ψ(a;k)=[1+μ_s a^s]Ψ_{\rm GR}(a;k)$ with a scale-independent $μ_s\simeq 0.09$ and $s\simeq 2$, while the anisotropic stress is negligibly small.
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Submitted 24 March, 2014;
originally announced March 2014.