Exploring stable models in $f(R; T; R_{\mu\nu} T^{\mu\nu})$ gravity

TL;DR

This paper investigates the stability of specific models in a complex modified gravity theory by analyzing perturbations in cosmological solutions, providing insights into their viability in describing the universe.

Contribution

It introduces a stability analysis framework for $f(R; T; R_{ ueta} T^{ ueta})$ gravity models using perturbation functions in Friedmann universe scenarios.

Findings

Stability conditions derived for de Sitter and power-law solutions.

Numerical solutions demonstrate stability or instability of particular models.

Framework applicable to a broad class of modified gravity theories.

Abstract

We examine in this paper the stability analysis in $f(R; T; R_{\mu\nu}T^{\mu\nu})$ modified gravity, where $R$ and $T$ are the Ricci scalar and the trace of the energy-momentum tensor, respectively. By considering the flat Friedmann universe, we obtain the corresponding generalized Friedmann equations and we evaluate the geometrical and matter perturbation functions. The stability is developed using the de Sitter and power-law solutions. We search for application the stability of two particular cases of $f(R; T; R_{\mu\nu}T^{\mu\nu})$ model by solving numerically the perturbation functions obtained.