Cosmological perturbations in a family of deformations of general relativity

We study linear cosmological perturbations in a previously introduced family of deformations of general relativity characterized by the absence of new degrees of freedom. The homogeneous and isotropic background in this class of theories is unmodified and is described by the usual Friedmann equations. The theory of cosmological perturbations is modified and the relevant deformation parameter has the dimension of length. Gravitational perturbations of the scalar type can be described by a certain relativistic potential related to the matter perturbations just as in general relativity. A system of differential equations describing the evolution of this potential and of the stress-energy density perturbations is obtained. We find that the evolution of scalar perturbations proceeds with a modified effective time-dependent speed of sound, which, contrary to the case of general relativity, does not vanish even at the matter-dominated stage. In a broad range of values of the length parameter controlling the deformation, a specific transition from the regime of modified gravity to the regime of general relativity in the evolution of scalar perturbations takes place during the radiation domination. In this case, the resulting power spectrum of perturbations in radiation and dark matter is suppressed on the comoving spatial scales that enter the Hubble radius before this transition. We estimate the bounds on the deformation parameter for which this suppression does not lead to observable consequences. Evolution of scalar perturbations at the inflationary stage is modified but very slightly and the primordial spectrum generated during inflation is not noticeably different from the one obtained in general relativity.Comment: 45 pages, version published in JCAP; minor changes, one section moved to the appendi

The nearly Newtonian regime in Non-Linear Theories of Gravity

The present paper reconsiders the Newtonian limit of models of modified gravity including higher order terms in the scalar curvature in the gravitational action. This was studied using the Palatini variational principle in [Meng X. and Wang P.: Gen. Rel. Grav. {\bf 36}, 1947 (2004)] and [Dom\'inguez A. E. and Barraco D. E.: Phys. Rev. D {\bf 70}, 043505 (2004)] with contradicting results. Here a different approach is used, and problems in the previous attempts are pointed out. It is shown that models with negative powers of the scalar curvature, like the ones used to explain the present accelerated expansion, as well as their generalization which include positive powers, can give the correct Newtonian limit, as long as the coefficients of these powers are reasonably small. Some consequences of the performed analysis seem to raise doubts for the way the Newtonian limit was derived in the purely metric approach of fourth order gravity [Dick R.: Gen. Rel. Grav. {\bf 36}, 217 (2004)]. Finally, we comment on a recent paper [Olmo G. J.: Phys. Rev. D {\bf 72}, 083505 (2005)] in which the problem of the Newtonian limit of both the purely metric and the Palatini formalism is discussed, using the equivalent Brans--Dicke theory, and with which our results partly disagree.Comment: typos corrected, replaced to match published versio

Non-Vacuum Bianchi Types I and V in f(R) Gravity

In a recent paper \cite{1}, we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f(R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to find energy density and pressure of the universe. In particular, we find two exact solutions in each case which correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.Comment: 15 pages, accepted for publication in Gen. Realtiv. Gravi

Chaotic scalar fields as models for dark energy

We consider stochastically quantized self-interacting scalar fields as suitable models to generate dark energy in the universe. Second quantization effects lead to new and unexpected phenomena is the self interaction strength is strong. The stochastically quantized dynamics can degenerate to a chaotic dynamics conjugated to a Bernoulli shift in fictitious time, and the right amount of vacuum energy density can be generated without fine tuning. It is numerically observed that the scalar field dynamics distinguishes fundamental parameters such as the electroweak and strong coupling constants as corresponding to local minima in the dark energy landscape. Chaotic fields can offer possible solutions to the cosmological coincidence problem, as well as to the problem of uniqueness of vacua.Comment: 30 pages, 3 figures. Replaced by final version accepted by Phys. Rev.

Accelerated Cosmological Models in First-Order Non-Linear Gravity

The evidence of the acceleration of universe at present time has lead to investigate modified theories of gravity and alternative theories of gravity, which are able to explain acceleration from a theoretical viewpoint without the need of introducing dark energy. In this paper we study alternative gravitational theories defined by Lagrangians which depend on general functions of the Ricci scalar invariant in minimal interaction with matter, in view of their possible cosmological applications. Structural equations for the spacetimes described by such theories are solved and the corresponding field equations are investigated in the Palatini formalism, which prevents instability problems. Particular examples of these theories are also shown to provide, under suitable hypotheses, a coherent theoretical explanation of earlier results concerning the present acceleration of the universe and cosmological inflation. We suggest moreover a new possible Lagrangian, depending on the inverse of sinh(R), which gives an explanation to the present acceleration of the universe.Comment: 23 pages, Revtex4 fil

Dark energy from conformal symmetry breaking

The breakdown of conformal symmetry in a conformally invariant scalar-tensor gravitational model is revisited in the cosmological context. Although the old scenario of conformal symmetry breaking in cosmology containing scalar field has already been used in many earlier works, it seems that no special attention has been paid for the investigation on the possible connection between the breakdown of conformal symmetry and the existence of dark energy. In this paper, it is shown that the old scenario of conformal symmetry breaking in cosmology, if properly interpreted, not only has a potential ability to describe the origin of dark energy as a symmetry breaking effect, but also may resolve the coincidence problem.Comment: 11 pages, minor revision, published online in EPJ

Crossing of the w=-1 Barrier in Two-Fluid Viscous Modified Gravity

Singularities in the dark energy late universe are discussed, under the assumption that the Lagrangian contains the Einstein term R plus a modified gravity term of the form R^\alpha, where \alpha is a constant. It is found, similarly as in the case of pure Einstein gravity [I. Brevik and O. Gorbunova, Gen. Rel. Grav. 37 (2005), 2039], that the fluid can pass from the quintessence region (w>-1) into the phantom region (w<-1) as a consequence of a bulk viscosity varying with time. It becomes necessary now, however, to allow for a two-fluid model, since the viscosities for the two components vary differently with time. No scalar fields are needed for the description of the passage through the phantom barrier.Comment: 16 pages latex, no figure

Phantom Field with O(N) Symmetry in Exponential Potential

In this paper, we study the phase space of phantom model with O(\emph{N}) symmetry in exponential potential. Different from the model without O(\emph{N}) symmetry, the introduction of the symmetry leads to a lower bound $w>-3$ on the equation of state for the existence of stable phantom dominated attractor phase. The reconstruction relation between the potential of O(\textit{N}) phantom system and red shift has been derived.Comment: 5 pages, 3 figures, replaced with the version to appear on Phys. Rev.

Generalized Second Law of Thermodynamics on the Event Horizon for Interacting Dark Energy

Here we are trying to find the conditions for the validity of the generalized second law of thermodynamics (GSLT) assuming the first law of thermodynamics on the event horizon in both cases when the FRW universe is filled with interacting two fluid system- one in the form of cold dark matter and the other is either holographic dark energy or new age graphic dark energy. Using the recent observational data we have found that GSLT holds both in quintessence era as well as in phantom era for new age graphic model while for holographic dark energy GSLT is valid only in phantom era.Comment: 8 pages, 2 figure