Generalised matter couplings in general relativity

TL;DR

This paper introduces a modified gravity theory where the volume form is dynamic, connecting it to unimodular gravity and Brans-Dicke theory, and explores its cosmological implications including accelerated expansion phases.

Contribution

It proposes a novel class of gravity models with a dynamical volume form, extending unimodular gravity and analyzing their cosmological behavior.

Findings

Existence of parameter ranges with accelerated expansion

Model exhibits a transition from acceleration to deceleration and back to acceleration

Dynamical systems analysis reveals rich cosmological dynamics

Abstract

A new class of modified theory of gravity is introduced where the volume form becomes dynamical. This approach is motivated by unimodular gravity and can also be related to Brans-Dicke theory. On the level of the action, the only change made will be through the volume element which is used in the integration. This is achieved by the introduction of a fourth order tensor which connects the spacetime metric to the new volume form. Using dynamical systems techniques, this model is studied in the context of cosmology. The most interesting result is that there exist parameter ranges where this model starts undergoing an epoch of accelerated expansion, followed by a decelerating expansion which evolves to a final epoch of accelerated expansion.