Non-linear Evolution of Matter Power Spectrum in Modified Theory of Gravity

We present a formalism to calculate the non-linear matter power spectrum in modified gravity models that explain the late-time acceleration of the Universe without dark energy. Any successful modified gravity models should contain a mechanism to recover General Relativity (GR) on small scales in order to avoid the stringent constrains on deviations from GR at solar system scales. Based on our formalism, the quasi non-linear power spectrum in the Dvali-Gabadadze-Porratti (DGP) braneworld models and $f(R)$ gravity models are derived by taking into account the mechanism to recover GR properly. We also extrapolate our predictions to fully non-linear scales using the Parametrized Post Friedmann (PPF) framework. In $f(R)$ gravity models, the predicted non-linear power spectrum is shown to reproduce N-body results. We find that the mechanism to recover GR suppresses the difference between the modified gravity models and dark energy models with the same expansion history, but the difference remains large at weakly non-linear regime in these models. Our formalism is applicable to a wide variety of modified gravity models and it is ready to use once consistent models for modified gravity are developed.Comment: 25 pages, 8 figures, comparison to N-body simulations in DGP added, published in PR

Cosmological Tests of Gravity

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories. The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ~kpc (galaxy scales) to ~Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the Integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages --- we summarize these tests and discuss the interesting prospects for new tests in the coming decade.Comment: Invited review for Annals of Physics; 58 pages, 8 figures

Large-Scale Structure in Brane-Induced Gravity II. Numerical Simulations

We use N-body simulations to study the nonlinear structure formation in brane-induced gravity, developing a new method that requires alternate use of Fast Fourier Transforms and relaxation. This enables us to compute the nonlinear matter power spectrum and bispectrum, the halo mass function, and the halo bias. From the simulation results, we confirm the expectations based on analytic arguments that the Vainshtein mechanism does operate as anticipated, with the density power spectrum approaching that of standard gravity within a modified background evolution in the nonlinear regime. The transition is very broad and there is no well defined Vainshtein scale, but roughly this corresponds to k_*~ 2 at redshift z=1 and k_*~ 1 at z=0. We checked that while extrinsic curvature fluctuations go nonlinear, and the dynamics of the brane-bending mode C receives important nonlinear corrections, this mode does get suppressed compared to density perturbations, effectively decoupling from the standard gravity sector. At the same time, there is no violation of the weak field limit for metric perturbations associated with C. We find good agreement between our measurements and the predictions for the nonlinear power spectrum presented in paper I, that rely on a renormalization of the linear spectrum due to nonlinearities in the modified gravity sector. A similar prediction for the mass function shows the right trends. Our simulations also confirm the induced change in the bispectrum configuration dependence predicted in paper I.Comment: 19 pages, 13 figures. v2: corrected typos, added more simulations, better test of predictions in large mass regime. v3: minor changes, published versio

A parametrization of the growth index of matter perturbations in various Dark Energy models and observational prospects using a Euclid-like survey

We provide exact solutions to the cosmological matter perturbation equation in a homogeneous FLRW universe with a vacuum energy that can be parametrized by a constant equation of state parameter $w$ and a very accurate approximation for the Ansatz $w(a)=w_0+w_a(1-a)$. We compute the growth index \gamma=\log f(a)/\log\Om_m(a), and its redshift dependence, using the exact and approximate solutions in terms of Legendre polynomials and show that it can be parametrized as $\gamma(a)=\gamma_0+\gamma_a(1-a)$ in most cases. We then compare four different types of dark energy (DE) models: $w\Lambda$CDM, DGP, $f(R)$ and a LTB-large-void model, which have very different behaviors at z\gsim1. This allows us to study the possibility to differentiate between different DE alternatives using wide and deep surveys like Euclid, which will measure both photometric and spectroscopic redshifts for several hundreds of millions of galaxies up to redshift $z\simeq 2$. We do a Fisher matrix analysis for the prospects of differentiating among the different DE models in terms of the growth index, taken as a given function of redshift or with a principal component analysis, with a value for each redshift bin for a Euclid-like survey. We use as observables the complete and marginalized power spectrum of galaxies $P(k)$ and the Weak Lensing (WL) power spectrum. We find that, using $P(k)$, one can reach (2%, 5%) errors in $(w_0, w_a)$, and (4%, 12%) errors in $(\gamma_0, \gamma_a)$, while using WL we get errors at least twice as large. These estimates allow us to differentiate easily between DGP, $f(R)$ models and $\Lambda$CDM, while it would be more difficult to distinguish the latter from a variable equation of state parameter or LTB models using only the growth index.}Comment: 29 pages, 7 figures, 6 table

Relativistic effects in galaxy clustering in a parametrized post-Friedmann universe

We explore the signatures of quintessence and modified gravity theories in the relativistic description of galaxy clustering within a parametrized post-Friedmann framework. For this purpose, we develop a calibration method to consistently account for horizon-scale effects in the linear parametrized Post-Friedmann perturbations of minimally and nonminimally coupled scalar-tensor theories and test it against the full model-specific fluctuations. We further study the relativistic effects in galaxy clustering for the normal and self-accelerating branches of the Dvali-Gabadadze-Porrati braneworld model as well as for phenomenological modifications of gravity. We quantify the impact of modified gravity and dark energy models on galaxy clustering by computing the velocity-to-matter density ratio F, the velocity contribution R, and the potential contribution P and give an estimate of their detectability in future galaxy surveys. Our results show that, in general, the relativistic correction contains additional information on gravity and dark energy, which needs to be taken into account in consistent horizon-scale tests of departures from LCDM using the galaxy-density field.Comment: 24 pages, 7 figures, 1 table; v2 matches published versio

Probing non-standard gravity with the growth index: a background independent analysis

Measurements of the growth index $\gamma(z)$ provide a clue as to whether Einstein's field equations encompass gravity also on large cosmic scales, those where the expansion of the universe accelerates. We show that the information encoded in this function can be satisfactorily parameterized using a small set of coefficients $\gamma_i$ in such a way that the true scaling of the growth index is recovered to better than $1\%$ in most dark energy and dark gravity models. We find that the likelihood of current data is maximal for $\gamma_0=0.74\pm 0.44$ and $\gamma_1=0.01\pm0.46$, a measurement compatible with the $\Lambda$CDM predictions. Moreover data favor models predicting slightly less growth of structures than the Planck LambdaCDM scenario. The main aim of the paper is to provide a prescription for routinely calculating, in an analytic way, the amplitude of the growth indices $\gamma_i$ in relevant cosmological scenarios, and to show that these parameters naturally define a space where predictions of alternative theories of gravity can be compared against growth data in a manner which is independent from the expansion history of the cosmological background. As the standard $\Omega$-plane provides a tool to identify different expansion histories $H(t)$ and their relation to various cosmological models, the $\gamma$-plane can thus be used to locate different growth rate histories $f(t)$ and their relation to alternatives model of gravity. As a result, we find that the Dvali-Gabadadze-Porrati gravity model is rejected with a $95\%$ confidence level. By simulating future data sets, such as those that a Euclid-like mission will provide, we also show how to tell apart LambdaCDM predictions from those of more extreme possibilities, such as smooth dark energy models, clustering quintessence or parameterized post-Friedmann cosmological models.Comment: 29 pages, 21 figure

Modified Gravity and Cosmology

In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f(R), general higher-order theories, Horava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.Comment: 312 pages, 15 figure