Energy Conditions and Stability in $f(R)$ theories of gravity with non-minimal coupling to matter

TL;DR

This paper investigates a new class of $f(R)$ gravity models with direct curvature-matter coupling, analyzing their viability through energy conditions and stability criteria to ensure physical plausibility.

Contribution

It introduces and studies the energy conditions and stability of $f(R)$ models with non-minimal curvature-matter coupling, a novel extension in modified gravity theories.

Findings

Models satisfy certain energy conditions under specific parameters.

Stability analysis shows conditions for avoiding Dolgov-Kawasaki instability.

Results support the physical viability of curvature-matter coupled $f(R)$ models.

Abstract

Recently, in the context of $f(R)$ modified theories of gravity, a new type of model has been proposed where one directly couples the scalar curvature to matter. As any model in $f(R)$ theory, there are certain conditions which have to be satisfy in order to ensure that the model is viable and physically meaningful. In this paper, one considers this new class of models with curvature-matter coupling and study them from the point of view of the energy conditions and of their stability under the Dolgov-Kawasaki criterion.