Constraining f(R)f(R) gravity models with disappearing cosmological constant

The $f(R)$ gravity models proposed by Hu-Sawicki and Starobinsky are generic for local gravity constraints to be evaded. The large deviations from these models either result into violation of local gravity constraints or the modifications are not distinguishable from cosmological constant. The curvature singularity in these models is generic but can be avoided provided that proper fine tuning is imposed on the evolution of scalaron in the high curvature regime. In principle, the problem can be circumvented by incorporating quadratic curvature correction in the Lagrangian though it might be quite challenging to probe the relevant region numerically.Comment: 9 pages and 4 figures, minor clarifications and corrections added, final version to appear in PR

How delicate are the f(R) gravity models with a disappearing cosmological constant?

We consider stability of spherically symmetric solutions in f(R) gravity model proposed by Starobinsky. We find that the model suffers from a severe fine-tuning problem when applied to compact objects like neutron stars. The problem can be remedied by introducing a cutoff on the mass of the scalar degree of freedom present in the model. A new mass scale associated with neutron stars density is then required for the stabilities of f(R) gravity solutions inside relativistic stars

Reheating the D-brane universe via instant preheating

We investigate a possibility of reheating in a scenario of D-brane inflation in a warped deformed conifold background which includes perturbative corrections to throat geometry sourced by chiral operator of dimension 3/2 in the CFT. The effective D-brane potential, in this case, belongs to the class of non-oscillatory models of inflation for which the conventional reheating mechanism does not work. We find that gravitational particle production is inefficient and leads to reheating temperature of the order of ${10^8} GeV$. We show that instant preheating is quite suitable to the present scenario and can easily reheat universe to a temperature which is higher by about three orders of magnitudes than its counter part associated with gravitational particle production. The reheating temperature is shown to be insensitive to a particular choice of inflationary parameters suitable to observations.Comment: 6 pages and 4 figures, replaced with revised version, to appear in PR

Generic f(R) theories and classicality of their scalarons

We study quantum stability bound on the mass of scalaron in generic theories of $f(R)$ gravity. We show that in these scenarios, the scalaron mass increases faster with local density of the environment than one loop quantum correction to it thereby leading to violation of quantum bound on the chameleon mass. The introduction of quadratic curvature corrections in the action are shown to stabilize the model.Comment: 7 pages, no figures, typos corrected, to match with the PLB published versio

Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters

We study the $f(R)$ theory of gravity using metric approach. In particular we investigate the recently proposed model by Hu-Sawicki, Appleby $-$ Battye and Starobinsky. In this model, the cosmological constant is zero in flat space time. The model passes both the Solar system and the laboratory tests. But the model parameters need to be fine tuned to avoid the finite time singularity recently pointed in the literature. We check the concordance of this model with the $H(z)$ and baryon acoustic oscillation data. We find that the model resembles the $\Lambda$CDM at high redshift. However, for some parameter values there are variations in the expansion history of the universe at low redshift.Comment: 16 pages and 9 figures, typos corrected, few references and minor clarifications added, revised version to appera in PR

Dark energy generated from a (super)string effective action with higher order curvature corrections and a dynamical dilaton

We investigate the possibility of a dark energy universe emerging from an action with higher-order string loop corrections to Einstein gravity in the presence of a massless dilaton. These curvature corrections (up to $R^4$ order) are different depending upon the type of (super)string model which is considered. We find in fact that Type II, heterotic, and bosonic strings respond differently to dark energy. A dark energy solution is shown to exist in the case of the bosonic string, while the other two theories do not lead to realistic dark energy universes. Detailed analysis of the dynamical stability of the de-Sitter solution is presented for the case of a bosonic string. A general prescription for the construction of a de-Sitter solution for the low-energy (super)string effective action is also indicated. Beyond the low-energy (super)string effective action, when the higher-curvature correction coefficients depend on the dilaton, the reconstruction of the theory from the universe expansion history is done with a corresponding prescription for the scalar potentials.Comment: 15 pages, 7 eps figures, minor corrections, published versio

Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity

In this paper we have investigated the cosmological dynamics of non-locally corrected gravity involving a function of the inverse d'Alembertian of the Ricci scalar, $f(\Box^{-1} R))$. Casting the dynamical equations into local form, we derive the fixed points of the dynamics and demonstrate the existence and stability of a one parameter family of dark energy solutions for a simple choice, $f(\Box^{-1} R)\sim \exp(\alpha \Box^{-1} R)$. The effective EoS parameter is given by, $w_{\rm eff}=({\alpha-1})/({3\alpha-1})$ and the stability of the solutions is guaranteed provided that $1/3<\alpha<2/3$. For $1/3<\alpha<1/2$ and $1/2<\alpha<2/3$, the underlying system exhibits phantom and non-phantom behavior respectively; the de Sitter solution corresponds to $\alpha=1/2$. For a wide range of initial conditions, the system mimics dust like behavior before reaching the stable fixed point. The late time phantom phase is achieved without involving negative kinetic energy fields. A brief discussion on the entropy of de Sitter space in non-local model is included.Comment: 5 pages and 2 figures, typos corrected, final version to appear in Phys. Lett.

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

Finite-time future singularities in modified Gauss-Bonnet and F(R,G)\mathcal{F}(R,G) gravity and singularity avoidance

We study all four types of finite-time future singularities emerging in late-time accelerating (effective quintessence/phantom) era from $\mathcal{F}(R,G)$-gravity, where $R$ and $G$ are the Ricci scalar and the Gauss-Bonnet invariant, respectively. As an explicit example of $\mathcal{F}(R,G)$-gravity, we also investigate modified Gauss-Bonnet gravity, so-called $F(G)$-gravity. In particular, we reconstruct the $F(G)$-gravity and $\mathcal{F}(R,G)$-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure the finite-time future singularities in $F(G)$-gravity and $\mathcal{F}(R,G)$-gravity by taking into account higher-order curvature corrections. The example of non-singular realistic modified Gauss-Bonnet gravity is presented. It turns out that adding such non-singular modified gravity to singular Dark Energy makes the combined theory to be non-singular one as well.Comment: 35 pages, no figure, published version, references adde