Further matters in space-time geometry: $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity

TL;DR

This paper explores a modified gravity model where matter non-minimally couples with geometry, deriving field equations, analyzing stability, and investigating cosmological solutions with potential implications for gravitational physics.

Contribution

It introduces a novel gravitational model with arbitrary functions of curvature and matter tensors, deriving equations of motion, stability conditions, and cosmological solutions.

Findings

Derived field equations for the model.

Identified stability conditions against perturbations.

Obtained analytical cosmological solutions.

Abstract

We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor with the matter energy-momentum tensor. The field equations of the model are obtained in the metric formalism, and the equation of motion of a massive test particle is derived. In this type of models the matter energy-momentum tensor is generally not conserved, and this non-conservation determines the appearance of an extra-force acting on the particles in motion in the gravitational field. The Newtonian limit of the model is also considered, and an explicit expression for the extra-acceleration which depends on the matter density is obtained in the small velocity limit for dust particles. We also analyze in detail the so-called Dolgov-Kawasaki instability, and obtain the stability conditions of the model with respect to local perturbations. A particular class of gravitational field equations can be obtained by imposing the conservation of the energy-momentum tensor. We derive the corresponding field equations for the conservative case by using a Lagrange multiplier method, from a gravitational action that explicitly contains an independent parameter multiplying the divergence of the energy-momentum tensor. The cosmological implications of the model are investigated for both the conservative and non-conservative cases, and several classes of analytical solutions are obtained.