Energy Conditions in $f(R,T,R_{\mu\nu}T^{\mu\nu})$ Gravity

TL;DR

This paper investigates the energy conditions in a novel modified gravity theory, deriving generalized inequalities and applying them to specific models, including stability analysis and special cases like $f(R,T)$ gravity.

Contribution

It introduces generalized energy conditions in $f(R,T,R_{}T^{})$ gravity and applies them to specific models, extending previous frameworks.

Findings

Derived more general energy conditions applicable to the new theory.

Applied conditions to exponential and power law models, analyzing stability.

Connected the new theory to $f(R,T)$ gravity as a special case.

Abstract

We discuss the validity of the energy conditions in a newly modified theory named as $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity, where $R$ and $T$ represent the scalar curvature and trace of the energy-momentum tensor. The corresponding energy conditions are derived which appear to be more general and can reduce to the familiar forms of these conditions in general relativity, $f(R)$ and $f(R,T)$ theories. The general inequalities are presented in terms of recent values of Hubble, deceleration, jerk and snap parameters. In particular, we use two specific models recently developed in literature to study concrete application of these conditions as well as Dolgov-Kawasaki instability. Finally, we explore $f(R,T)$ gravity as a specific case to this modified theory for exponential and power law models.