Conservation laws in theories with universal gravity/matter coupling

TL;DR

This paper explores the conservation laws in theories with universal gravity/matter coupling, revealing equivalences for perfect fluids and analyzing cases without assuming matter current conservation.

Contribution

It demonstrates the equivalence between energy density assumptions and matter current conservation for perfect fluids, and investigates conservation laws without such assumptions.

Findings

Equivalence between $ ext{L}_m=- ext{ε}$ and matter current conservation for perfect fluids

Analysis of conservation laws without assuming matter fluid current conservation

Insights into the behavior of particles in universal gravity/matter coupling theories

Abstract

In this paper, we investigate the conservation laws of different type of particles in theories with a universal gravity/matter coupling. The result brings new insights about previous studies on universal gravity/matter theories. Especially, the paper demonstrates that for perfect fluids, there is an equivalence between the assumption $\L_m=-\epsilon$, where $\epsilon$ is the total energy density; and the assumption that the matter fluid current is conserved ($\nabla_\sigma (\rho u^\sigma)=0$, where $\rho$ is the rest mass density). However, the main result is given in the general case where one does not make any assumption on the conservation of the matter fluid current.