The canonical energy-momentum currents in cosmology

TL;DR

This paper discusses a covariant approach to defining conserved energy-momentum currents in cosmology, unifying different formulations of gravity and linking to known mass concepts.

Contribution

It introduces a covariant, frame-independent method for defining energy-momentum currents that unifies Einstein's formulations and relates to the Kodama vector and Misner-Sharp mass.

Findings

Conserved energy-momentum currents can be defined without Killing symmetries.

The canonical time direction aligns with the Kodama vector in cosmology.

The Noether energy matches the Misner-Sharp mass.

Abstract

The parallel theory of relativity predicts conserved energy-momentum currents for an arbitrary metric, without invoking Killing symmetries. By treating the reference frame as an independent variational field and requiring it to carry no energy, the theory naturally unifies Einstein's two formulations of gravity and yields uniquely defined covariant charges. In isotropic and homogeneous cosmology, the canonical time direction selected by the reference frame coincides with the Kodama vector, and the associated Noether energy reproduces the Misner-Sharp mass.