Physical aspects of modified gravity theories

Abstract

The paper extends basic Einstein--Hilbert action by adding an 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.

Are f(R, Matter) theories really relevant to cosmology?

“…It uses non-universal couplings of gravity with the matter sector, via the curvature tensor. We henceforth call this class f (R, Matter) theories, and gather under this name f (R, T ) gravity [8] and its variants such as f (R, L m ) [9], f (R, T, T µν R µν ) [10,11], f (R, T µν T µν ) [12] and JCAP05(2024)064 f (R, G µν T µν ) [13]. To be fully explicit, the theories of this class are defined by replacing the Ricci scalar R of the Einstein-Hilbert action (1.1) by a function of the curvature tensor and the matter Lagrangian:…”