Investigating new forms of gravity-matter couplings in the gravitational field equations

TL;DR

This paper introduces a modified gravity model with new matter couplings in Einstein's equations, analyzing its implications for cosmology and black hole solutions, and exploring its potential to address dark sector phenomena.

Contribution

It proposes a novel gravity-matter coupling term involving the Ricci tensor and energy-momentum tensor, extending Einstein's equations with a correction linear in Planck's length.

Findings

The model reduces to general relativity in vacuum.

Solutions are obtained for specific metrics including Schwarzschild and FLRW.

The effective energy-momentum tensor includes dark sector-like components.

Abstract

This paper proposes a toy model where, in the Einstein equations, the right-hand side is modified by the addition of a term proportional to the symmetrized partial contraction of the Ricci tensor with the energy-momentum tensor, while the left-hand side remains equal to the Einstein tensor. Bearing in mind the existence of a natural length scale given by the Planck length, dimensional analysis shows that such a term yields a correction linear in h to the classical term, that is instead just proportional to the energy-momentum tensor. One then obtains an effective energy-momentum tensor that consists of three contributions: pure energy part, mechanical stress and thermal part. The pure energy part has the appropriate property for dealing with the dark sector of modern relativistic cosmology. Such a theory coincides with general relativity in vacuum, and the resulting field equations are here solved for a Dunn and Tupper metric, for departures from an interior Schwarzschild solution as well as for a Friedmann-Lemaitre-Robertson-Walker universe.