Conditions and instability in $f(R)$ gravity with non-minimal coupling between matter and geometry

TL;DR

This paper investigates four classes of generalized $f(R)$ gravity models with non-minimal matter-geometry coupling, analyzing conditions for cosmic acceleration and stability, particularly focusing on late-time acceleration and Dolgov-Kawasaki instability.

Contribution

It introduces and studies four specific classes of $f(R)$ gravity models with non-minimal coupling, exploring their viability for cosmic acceleration and stability conditions.

Findings

Identifies conditions for late-time cosmic acceleration in the models.

Analyzes the relationship among parameters p, w, and n.

Examines the Dolgov-Kawasaki stability criterion for each model.

Abstract

In this paper on the basis of the generalized $f(R)$ gravity model with arbitrary coupling between geometry and matter, four classes of $f(R)$ gravity models with non minimal coupling between geometry and matter will be studied. By means of conditions of power law expansion and the equation of state of matter less than -1/3, the relationship among p, w and n, the conditions and the candidate for late time cosmic accelerated expansion will be discussed in the four classes of $f(R)$ gravity models with non minimal coupling. Furthermore, in order to keep considering models to be realistic ones, the Dolgov Kawasaki instability will be investigated in each of them.