Physical aspects of ${f}(R,G_{\mu \nu}T^{\mu \nu})$ modified gravity theories

TL;DR

This paper explores a modified gravity theory involving a new invariant coupling between geometry and matter, analyzing its cosmological implications and compatibility with different universe evolution stages.

Contribution

It introduces a novel ${f}(R,G_{ u ho}T^{ u ho})$ gravity model with non-minimal matter-geometry coupling and studies its cosmological dynamics.

Findings

Model compatible with multiple cosmic epochs

Potential to explain late-time universe behavior

Dynamical system analysis reveals stable solutions

Abstract

The paper extends basic Einstein--Hilbert action by adding a newly proposed invariant constructed from a specific contraction between the Einstein tensor and the energy momentum tensor, encoding a non--minimal coupling between the space--time geometry and the matter fields. The fundamental Einstein--Hilbert action is extended by considering a generic function ${f}(R,G_{\mu \nu}T^{\mu \nu})$ which is further decomposed into its main constituents, a geometric component which depends on the scalar curvature, and a second element embedding the interplay between geometry and matter fields. Specific cosmological models are established at the level of background dynamics, based on particular couplings between the matter energy--momentum tensor and the Einstein tensor. After deducing the resulting field equations, the physical aspects for the cosmological model are investigated by employing a dynamical system analysis for various coupling functions. The investigation showed that the present model is compatible with different epochs in the evolution of our Universe, possible explaining various late time historical stages.