Cosmological perturbations and observational constraints on nonlocal massive gravity

Nonlocal massive gravity can provide an interesting explanation for the late-time cosmic acceleration, with a dark energy equation of state $w_{\rm DE}$ smaller than $-1$ in the past. We derive the equations of linear cosmological perturbations to confront such models with the observations of large-scale structures. The effective gravitational coupling to nonrelativistic matter associated with galaxy clusterings is close to Newton's gravitational constant $G$ for a mass scale $m$ slightly smaller than today's Hubble parameter $H_0$. Taking into account the background expansion history as well as the evolution of matter perturbations $\delta_m$, we test for these models with Type Ia Supernovae (SnIa) from Union 2.1, the cosmic microwave background (CMB) measurements from Planck, a collection of baryon acoustic oscillations (BAO), and the growth rate data of $\delta_m$. Using a higher value of $H_0$ derived from its direct measurement ($H_0 \gtrsim 70$ km s$^{-1}$ Mpc$^{-1}$) the data strongly support the nonlocal massive gravity model ($-1.1 \lesssim w_{\rm DE} \lesssim -1.04$ in the past) over the $\Lambda$CDM model ($w_{\rm DE}=-1$), whereas for a lower prior (67 km s$^{-1}$ Mpc$^{-1}$ $\lesssim$ $H_0 \lesssim 70$ km s$^{-1}$ Mpc$^{-1}$) the two models are statistically comparable.Comment: 16 pages, 6 figures, changes match published versio

Accuracy of the growth index in the presence of dark energy perturbations

We present the analytical solutions for the evolution of matter density perturbations, for a model with a constant dark energy equation of state $w$ but when the effects of the dark energy perturbations are properly taken into account. We consider two cases, the first when the sound speed of the perturbations is zero $c_s^2=0$ and the general case $0<c_s^2 \leq 1$. In the first case our solution is exact, while in the second case we found an approximate solution which works to better than $0.3\%$ accuracy for $k>10 H_0$ or equivalently $k/h>0.0033 \textrm{Mpc}^{-1}$. We also estimate the corrections to the growth index $\gamma(z)$, commonly used to parametrize the growth-rate. We find that these corrections due to the DE perturbations affect the growth index $\gamma$ at the $3\%$ level. We also compare our new expressions for the growth index with other expressions already present in the literature and we find that the latter are less accurate than the ones we propose here. Therefore, our analytical calculations are necessary as the theoretical predictions for the fundamental parameters to be constrained by the upcoming surveys need to be as accurate as possible, especially since we are entering in the precise cosmology era where parameters will be measured to the percent level.Comment: 8 pages, 4 figure

Cosmological constraints and comparison of viable f(R)f(R) models

In this paper we present cosmological constraints on several well-known $f(R)$ models, but also on a new class of models that are variants of the Hu-Sawicki one of the form $f(R)=R-\frac{2\Lambda}{1+b\;y(R,\Lambda)}$, that interpolate between the cosmological constant model and a matter dominated universe for different values of the parameter $b$, which is usually expected to be small for viable models and which in practice measures the deviation from General Relativity. We use the latest growth rate, Cosmic Microwave Background, Baryon Acoustic Oscillations, Supernovae type Ia and Hubble parameter data to place stringent constraints on the models and to compare them to the cosmological constant model but also other viable $f(R)$ models such as the Starobinsky or the degenerate hypergeometric models. We find that these kinds of Hu-Sawicki variant parameterizations are in general compatible with the currently available data and can provide useful toy models to explore the available functional space of $f(R)$ models, something very useful with the current and upcoming surveys that will test deviations from General Relativity.Comment: 12 pages, 5 figures, 6 tables. Comments welcome. Changes match published versio

Observational constraints on viable f(R) parametrizations with geometrical and dynamical probes

We demonstrate that a wide range of viable f(R) parameterizations (including the Hu & Sawicki and the Starobinsky models) can be expressed as perturbations deviating from the LCDM Lagrangian. We constrain the deviation parameter b using a combination of geometrical and dynamical observational probes. In particular, we perform a joint likelihood analysis of the recent Supernovae Type Ia data, the Cosmic Microwave Background shift parameters, the Baryonic Acoustic Oscillations and the growth rate data provided by the various galaxy surveys. This analysis provides constraints for the following parameters: the matter density Omega_{m0}, the deviation from LCDM parameter b and the growth index gamma(z). We parametrize the growth index gamma(z) in three manners (constant, Taylor expansion around z=0, and Taylor expansion around the scale factor). We point out the numerical difficulty for solving the generalized f(R) Friedman equation at high redshifts due to stiffness of the resulting ordinary differential equation. We resolve this problem by constructing an efficient analytical perturbative method in the deviation parameter b. We demonstrate that this method is highly accurate, by comparing the resulting analytical expressions for the Hubble parameter, with the numerical solutions at low and intermediate redshifts. Surprisingly, despite of its perturbative nature, the accuracy of the method persists even for values of b that are of O(1).Comment: 20 pages, 10 figures. Published in Phys. Rev. D. Added 2 Figures and new comments. The Mathematica and data files used for the numerical analysis of this study may be downloaded from: http://leandros.physics.uoi.gr/fr-constraints/probes.ht