Bounce cosmology in f({mathcal {R}}) gravity

M Ilyas,W U Rahman

doi:10.1140/epjc/s10052-021-08955-7

Abstract

In this paper, we analyze the modified f({mathcal {R}}) gravity models in Friedmann–Lemaître–Robertson–Walker (FLRW) background. The actions of bouncing cosmology are studied under consideration of different viable models in f({mathcal {R}}) gravity theory that can resolve the difficulty of singularity in standard Big-Bang cosmology. Under different viable models in f({mathcal {R}}) gravity theory, the cosmological constraints are plotted in provisions of cosmic-time, then investigated the bounce circumstance. In addition, the red-shift parameter is used to reconstruct the modified gravity, and compile the cosmological parameters that infer accelerated universe expansion. Finally, the situation stability is evaluated with a sound speed feature, which illustrates late-time stability.

Highlights

General theory of relativity has explained many specification of universe by the various theories and observational evidence
In terms of cosmic-time, we studied bouncing behavior for four different viable models in f (R) gravity for the scenario and acquired bouncing state at bounce stage and illustrated the related cosmological parameters
We rebuilt the model with a red-shift component, and we are using the r (z) function parametrization, and the cosmological parameters were written in terms of red-shift z, the Friedmann equations and the effective equation of state (EoS)

Summary

Introduction

General theory of relativity has explained many specification of universe by the various theories and observational evidence. Bouncing universe is the new idea, suggested to resolves the singularity problem in big bang cosmology [8,9]. In the big bang theory, we will avoid the starting singularity by bouncing model with the advantage of different models in modified f (R) theory. From the above discussion we say that the dark energy that is reconstructed by red shift parameter is a source of f (R) gravity. We study the modified f (R) gravity and solve the field equations for FLRW metric in the framework of perfect fluid in Sect. 2. While, we analyze the bouncing behavior by the Hubble parameter and scale-factor, by assuming different models in f (R) gravity. Which is known as the Ricci algebraic equation after selecting any viable formulations of modified f (R) gravity model.

Reconstruction method for power-law model

Reconstruction by red-shift parameter

Stability analysis

Findings

Summary