Energy, momentum and angular momentum conservations in de Sitter gravity

TL;DR

This paper derives two types of conservation laws in de Sitter gravity, uniting energy-momentum and angular momentum tensors, and discusses observable effects of the inherent parts of these currents.

Contribution

It introduces a new framework for conservation laws in de Sitter gravity, uniting matter and gravitational currents, and highlights the observable impact of the inherent parts of energy-momentum and angular momentum.

Findings

A differential equation for a dS-covariant current uniting EM and AM tensors.

A dS-invariant current conserved with vanishing torsion-free divergence.

The inherent part of the EM tensor affects dust particle trajectories.

Abstract

In de Sitter (dS) gravity, where gravity is a gauge field introduced to realize the local dS invariance of the matter field, two kinds of conservation laws are derived. The first kind is a differential equation for a dS-covariant current, which unites the canonical energy-momentum (EM) and angular momentum (AM) tensors. The second kind presents a dS-invariant current which is conserved in the sense that its torsion-free divergence vanishes. The dS-invariant current unites the total (matter plus gravity) EM and AM currents. It is well known that the AM current contains an inherent part, called the spin current. Here it is shown that the EM tensor also contains an inherent part, which might be observed by its contribution to the deviation of the dust particle's world line from a geodesic. All the results are compared to the ordinary Lorentz gravity.