Amare Abebe

On f(R) gravity in scalar–tensor theories

We study f(R) gravity models in the language of scalar–tensor (ST) theories. The correspondence between f(R) gravity and ST theories is revisited since f(R) gravity is a subclass of Brans–Dicke models, with a vanishing coupling constant (ω = 0). In this treatment, four f(R) toy models are used to analyze the early-universe cosmology, when the scalar field ϕ dominates over standard matter. We have obtained solutions to the Klein–Gordon equation for those models. It is found that for the first model (f(R) = βRn), as time increases the scalar field decreases and decays asymptotically. For the second model (f(R)=αR+βRn), it was found that the function ϕ(t) crosses the t-axis at different values for different values of β. For the third model f(R) = R −ν4 R , when the value of ν is small, the potential V (ϕ) behaves like the standard inflationary potential. For the fourth model (f(R) = R−(1−m)ν2 R ν2 m − 2Λ), we show that there is a transition between 1.5 1.55. The slow-roll approximation is applied to each of the four f(R) models and we obtain the respective expressions for the spectral index ns and the tensor-to-scalar ratio r.

Shear-free anisotropic cosmological models in {\varvec{f}\,\varvec{(R)}} gravity

We study a class of shear-free, homogeneous but anisotropic cosmological models with imperfect matter sources in the context of f(R) gravity. We show that the anisotropic stresses are related to the electric part of the Weyl tensor in such a way that they balance each other. We also show that within the class of orthogonal f(R) models, small perturbations of shear are damped, and that the electric part of the Weyl tensor and the anisotropic stress tensor decay with the expansion as well as the heat flux of the curvature fluid. Specializing in locally rotationally symmetric spacetimes in orthonormal frames, we examine the late-time behaviour of the de Sitter universe in f(R) gravity. For the Starobinsky model of f(R), we study the evolutionary behavior of the Universe by numerically integrating the Friedmann equation, where the initial conditions for the expansion, acceleration and jerk parameters are taken from observational data.

Chaplygin-gas Solutions of f(R) Gravity

We explore exact f(R) gravity solutions that mimic Chaplygin-gas inspired LCDM cosmology. Starting with the original and modified Chaplygin gas equations of state, we reconstruct the forms of f(R) Lagrangians. The resulting solutions are generally quadratic in the Ricci scalar, but have appropriate LCDM solutions in limiting cases. These solutions, given appropriate initial conditions, can be potential candidates for scalar field-driven early universe expansion (inflation) and dark energy-driven late-time cosmic acceleration.

Irrotational-fluid cosmologies in fourth-order gravity

In this paper, we explore classes of irrotational-fluid cosmological models in the context of f(R)-gravity in an attempt to put some theoretical and mathematical restrictions on the form of the f(R) gravitational Lagrangian. In particular, we investigate the consistency of linearised dust models for shear-free cases as well as in the limiting cases when either the gravito-magnetic or gravito-elecric components of the Weyl tensor vanish. We also discuss the existence and consistency of classes of non-expanding irrotational spacetimes in f(R)-gravity.

A Generalized Solution of Bianchi Type-V Models with Time-Dependent G and Λ

We study the homogeneous but anisotropic Bianchi type-V cosmological model with time-dependent gravitational and cosmological “constants”. Exact solutions of the Einstein field equations (EFEs) are presented in terms of adjustable parameters of quantum field theory in a spatially curved and expanding background. It has been found that the general solution of the average scale factor a as a function of time involved the hypergeometric function. Two cosmological models are obtained from the general solution of the hypergeometric function and the Emden–Fowler equation. The analysis of the models shows that, for a particular choice of parameters in our first model, the cosmological “constant” decreases whereas the Newtonian gravitational “constant” increases with time, and for another choice of parameters, the opposite behaviour is observed. The models become isotropic at late times for all parameter choices of the first model. In the second model of the general solution, both the cosmological and gravitational “constants” decrease while the model becomes more anisotropic over time. The exact dynamical and kinematical quantities have been calculated analytically for each model.

Anisotropic solutions in modified gravity

Anisotropic but homogeneous, shear-free cosmological models with imperfect matter sources in f(R) gravity are investigated. The relationship between the anisotropic stresses and the electric part of the Weyl tensor, as well as their evolutions in orthogonal f(R) models, is explored. The late-time behaviour of the de Sitter universe (as an example of a locally rotationally symmetric spacetimes in orthonormal frames) in f(R) gravity is examined. By taking initial conditions for the expansion, acceleration and jerk parameters from observational data, numerical integrations for the evolutionary behavior of the Universe in the Starobinsky model of f(R) have been carried out.

A study of perturbations in scalar–tensor theory using 1 + 3 covariant approach

This work discusses scalar-tensor theories of gravity, with a focus on the Brans-Dicke subclass, and one that also takes note of the latters equivalence with

Reconstructing f(R) gravity from a Chaplygin scalar field in de Sitter spacetimes

f(R)

Inflationary f (R) Cosmologies

gravitation theories. A 1+3 covariant formalism is used in this case to discuss covariant perturbations on a background Friedmann-Laimaitre-Robertson-Walker (FLRW) space-time. Linear perturbation equations are developed, based on gauge-invariant gradient variables. Both scalar and harmonic decompositions are applied to obtain second-order equations. These equations can then be used for further analysis of the behavior of the perturbation quantities in such a scalar-tensor theory of gravitation. Energy density perturbations are studied for two systems, namely for a scalar fluid-radiation system and for a scalar fluid-dust system, for

Inflation constraints for classes of f(R) models

R^{n}