Background cosmological dynamics in $f(R)$ gravity and observational constraints

TL;DR

This paper investigates the background cosmological evolution in $f(R)$ gravity models, identifying two distinct regimes and using observational parameters and statefinder diagnostics to characterize their behavior.

Contribution

It introduces a method to analyze $f(R)$ models using autonomous systems and statefinder parameters, highlighting their dynamic regimes and observational signatures.

Findings

Models exhibit a phantom phase followed by quintessence-like behavior.

Statefinder parameters effectively distinguish these $f(R)$ models.

The study provides a framework for comparing $f(R)$ models with observational data.

Abstract

In this paper, we carry out a study of viable cosmological models in $f(R)$-gravity at the background level. We use observable parameters like $\Omega$ and $\gamma$ to form autonomous system of equations and show that the models under consideration exhibit two different regimes in their time evolution, namely, a phantom phase followed by a quintessence like behavior. We employ statefinder parameters to emphasize a characteristic discriminative signature of these models.