New class of generalized coupling theories

TL;DR

This paper introduces a novel class of gravity theories with matter-dependent couplings, which behave like general relativity in vacuum but differ within matter, affecting gravitational wave speed and cosmic evolution.

Contribution

The paper develops a new class of gravity theories with matter-coupled metrics, providing a framework that matches GR in vacuum but exhibits unique matter interactions and cosmological implications.

Findings

Gravitational wave speed in matter differs from vacuum in these theories.

Cosmological models include inflationary and dark energy-like phases.

Theories are constrained by gravitational wave observations.

Abstract

We propose a new class of gravity theories which are characterized by a nontrivial coupling between the gravitational metric and matter mediated by an auxiliary rank-2 tensor. The actions generating the field equations are constructed so that these theories are equivalent to general relativity in a vacuum, and only differ from general relativity theory within a matter distribution. We analyze in detail one of the simplest realizations of these generalized coupling theories. We show that in this case the propagation speed of gravitational radiation in matter is different from its value in vacuum and that this can be used to weakly constrain the (single) additional parameter of the theory. An analysis of the evolution of homogeneous and isotropic spacetimes in the same framework shows that there exist cosmic histories with both an inflationary phase and a dark era characterized by a different expansion rate.