Consistency of f(R)=R2−R02f(R)=\sqrt{R^{2}-R_{0}^2} Gravity with the Cosmological Observations in Palatini Formalism

In this work we study the dynamics of universe in $f(R)=\sqrt{R^2-R_{0}^2}$ modified gravity with Palatini formalism. We use data from recent observations as Supernova Type Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS) data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and large scale structure formation (LSS) from the 2dFGRS survey to put constraint on the parameters of the model. To check the consistency of this action, we compare the age of old cosmological objects with the age of universe. In the combined analysis with the all the observations, we find the parameters of model as $R_0=6.192_{-0.177}^{+0.167}\times H_0^2$ and $\Omega_m=0.278_{-0.278}^{+0.273}$.Comment: 12 pages, 7 figure

The Distinguishability of Interacting Dark Energy from Modified Gravity

We study the observational viability of coupled quintessence models with their expansion and growth histories matched to modified gravity cosmologies. We find that for a Dvali-Gabadadze-Porrati model which has been fitted to observations, the matched interacting dark energy models are observationally disfavoured. We also study the distinguishability of interacting dark energy models matched to scalar-tensor theory cosmologies and show that it is not always possible to find a physical interacting dark energy model which shares their expansion and growth histories.Comment: 8 pages, 5 figure

Parametrization for the Scale Dependent Growth in Modified Gravity

We propose a scale dependent analytic approximation to the exact linear growth of density perturbations in Scalar-Tensor (ST) cosmologies. In particular, we show that on large subhorizon scales, in the Newtonian gauge, the usual scale independent subhorizon growth equation does not describe the growth of perturbations accurately, as a result of scale-dependent relativistic corrections to the Poisson equation. A comparison with exact linear numerical analysis indicates that our approximation is a significant improvement over the standard subhorizon scale independent result on large subhorizon scales. A comparison with the corresponding results in the Synchronous gauge demonstrates the validity and consistency of our analysis.Comment: 10 pages, 5 figures. Minor modifications and references added to match published versio

A new approach to cosmological perturbations in f(R) models

We propose an analytic procedure that allows to determine quantitatively the deviation in the behavior of cosmological perturbations between a given f(R) modified gravity model and a LCDM reference model. Our method allows to study structure formation in these models from the largest scales, of the order of the Hubble horizon, down to scales deeply inside the Hubble radius, without employing the so-called "quasi-static" approximation. Although we restrict our analysis here to linear perturbations, our technique is completely general and can be extended to any perturbative order.Comment: 21 pages, 2 figures; Revised version according to reviewer's suggestions; Typos corrected; Added Reference

Dynamics of f(R)-cosmologies containing Einstein static models

We study the dynamics of homogeneous isotropic FRW cosmologies with positive spatial curvature in $f(R)$-gravity, paying special attention to the existence of Einstein static models and only study forms of $f(R)=R^n$ for which these static models have been shown to exist. We construct a compact state space and identify past and future attractors of the system and recover a previously discovered future attractor corresponding to an expanding accelerating model. We also discuss the existence of universes which have both a past and future bounce, a phenomenon which is absent in General Relativity.Comment: 14 pages, 6 figure

Geometric and thermodynamic properties in Gauss-Bonnet gravity

In this paper, the generalized second law (GSL) of thermodynamics and entropy is revisited in the context of cosmological models in Gauss-Bonnet gravity with the boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. The model is best fitted with the observational data for distance modulus. The best fitted geometric and thermodynamic parameters such as equation of state parameter, deceleration parameter and entropy are derived. To link between thermodynamic and geometric parameters, the "entropy rate of change multiplied by the temperature" as a model independent thermodynamic state parameter is also derived. The results show that the model is in good agreement with the observational analysis.Comment: 13 pages, 13 figures, to be published in Astrophysics and Space Sc

Interacting Ghost Dark Energy in Non-Flat Universe

A new dark energy model called "ghost dark energy" was recently suggested to explain the observed accelerating expansion of the universe. This model originates from the Veneziano ghost of QCD. The dark energy density is proportional to Hubble parameter, $\rho_D=\alpha H$, where $\alpha$ is a constant of order $\Lambda_{\rm QCD}^3$ and $\Lambda_{\rm QCD}\sim 100 MeV$ is QCD mass scale. In this paper, we extend the ghost dark energy model to the universe with spatial curvature in the presence of interaction between dark matter and dark energy. We study cosmological implications of this model in detail. In the absence of interaction the equation of state parameter of ghost dark energy is always $w_D > -1$ and mimics a cosmological constant in the late time, while it is possible to have $w_D < -1$ provided the interaction is taken into account. When $k = 0$, all previous results of ghost dark energy in flat universe are recovered. To check the observational consistency, we use Supernova type Ia (SNIa) Gold sample, shift parameter of Cosmic Microwave Background radiation (CMB) and the Baryonic Acoustic Oscillation peak from Sloan Digital Sky Survey (SDSS). The best fit values of free parameter at $1\sigma$ confidence interval are: $\Omega_m^0= 0.35^{+0.02}_{-0.03}$, $\Omega_D^0=0.75_{-0.04}^{+0.01}$ and $b^2=0.08^{+0.03}_{-0.03}$. Consequently the total energy density of universe at present time in this model at 68% level equates to $\Omega_{\rm tot}^0=1.10^{+0.02}_{-0.05}$.Comment: 19 pages, 9 figures. V2: Added comments, observational consequences, references, figures and major corrections. Accepted for publication in General Relativity and Gravitatio

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Entropy and statefinder diagnosis in chameleon cosmology

In this paper, the generalized second law (GSL) of thermodynamics and entropy is revisited in the context of cosmological models with bouncing behavior such as chameleon cosmology where the boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. From a thermodynamic point of view, to link between thermodynamic and geometric parameters in cosmological models, we introduce "entropy rate of change multiplied by the temperature" as a model independent thermodynamic state parameter together with the well known $\{r,s \}$ statefinder to differentiate the dark energy models.Comment: 11 pages, 5 figures. will be published in Astrophys. Space Sc