Stellar configurations in f(R) theories of gravity

We study stellar configurations and the space-time around them in metric $f(R)$ theories of gravity. In particular, we focus on the polytropic model of the Sun in the $f(R)=R-\mu^4/R$ model. We show how the stellar configuration in the $f(R)$ theory can, by appropriate initial conditions, be selected to be equal to that described by the Lane-Emden -equation and how a simple scaling relation exists between the solutions. We also derive the correct solution analytically near the center of the star in $f(R)$ theory. Previous analytical and numerical results are confirmed, indicating that the space-time around the Sun is incompatible with Solar System constraints on the properties of gravity. Numerical work shows that stellar configurations, with a regular metric at the center, lead to $\gamma_{PPN}\simeq1/2$ outside the star ie. the Schwarzschild-de Sitter -space-time is not the correct vacuum solution for such configurations. Conversely, by selecting the Schwarzschild-de Sitter -metric as the outside solution, we find that the stellar configuration is unchanged but the metric is irregular at the center. The possibility of constructing a $f(R)$ theory compatible with the Solar System experiments and possible new constraints arising from the radius-mass -relation of stellar objects is discussed.Comment: 8 pages, 7 figures; typos corrected, reference adde

Consistency of f(R)f(R) gravity models around solar polytropes

It is stated that a class of $f(R)$ gravity models seem to obtain $\Lambda$CDM behaviour for high redshifts and general relativistic behaviour locally at high curvatures. In the present paper, we numerically study polytropic configurations that resemble stars like young sun with Hu and Sawicki $f(R)$ gravity field equations and compare the spacetime at the boundary to the general relativistic counterpart. These polytropes are stationary spherically symmetric configurations and have regular metrics at the origin. Since Birkhoff's theorem does not apply for modified gravity, the solution outside may deviate from Schwarzschild-de Sitter spacetime. At the boundary, Post-Newtonian parametrization was used to determine how much the studied model deviates from the general relativistic $\Lambda$CDM model.Comment: 10 pages, 3 figures, text revised for publicatio

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

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