Notes on dark energy interacting with dark matter and unparticle in loop quantum cosmology

We investigate the behavior of dark energy interacting with dark matter and unparticle in the framework of loop quantum cosmology. In four toy models, we study the interaction between the cosmic components by choosing different coupling functions representing the interaction. We found that there are only two attractor solutions namely dark energy dominated and dark matter dominated Universe. The other two models are unstable, as they predict either a dark energy filled Universe or one completely devoid of it.Comment: 9 pages, 10 figures. v2: Minor revisions, matches published versio

Equations of State in the Brans-Dicke cosmology

We investigate the Brans-Dicke (BD) theory with the potential as cosmological model to explain the present accelerating universe. In this work, we consider the BD field as a perfect fluid with the energy density and pressure in the Jordan frame. Introducing the power-law potential and the interaction with the cold dark matter, we obtain the phantom divide which is confirmed by the native and effective equation of state. Also we can describe the metric $f(R)$ gravity with an appropriate potential, which shows a future crossing of phantom divide in viable $f(R)$ gravity models when employing the native and effective equations of state.Comment: 23 pages, 7 figure

The Schro¨\ddot{o}dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics

In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schr$\ddot{o}$dinger-Poisson equations in the large $N$ limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as $\hbar \sim M^{5/3} G^{1/2} (N/)^{1/6}$, where is $G$ the gravitational constant, $N$ and $M$ are the number and the mass of the bodies, and $$ is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schr$\ddot{o}$dinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales.Comment: Accepted for publication in the Euro. Phys. J.

On the true nature of renormalizability in Horava-Lifshitz gravity

We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.Comment: Latex file in Revtex style, 5 pages, no figures. v2: references added, version accepted for publication in Foundations of Physic

Screening of cosmological constant for De Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities

We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom-like phases. In particular, it is found that there is a case in which a crossing of the phantom divide from the non-phantom (quintessence) phase to the phantom one can be realized when a finite-time future singularity occurs. Moreover, it is demonstrated that the addition of an $R^2$ term can cure the finite-time future singularities in non-local gravity. It is also suggested that in the framework of non-local gravity, adding an $R^2$ term leads to possible unification of the early-time inflation with the late-time cosmic acceleration.Comment: 42 pages, no figure, version 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

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

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