Energy-Momentum of the Friedmann Models in General Relativity and Teleparallel Theory of Gravity

TL;DR

This paper evaluates the energy-momentum distribution in Friedmann cosmological models using Møller's prescriptions in both General Relativity and Teleparallel Gravity, revealing partial consistency and specific energy behaviors.

Contribution

It compares energy-momentum densities in Friedmann models within GR and teleparallel theory, showing independence from teleparallel coupling constants.

Findings

Energy density vanishes at specific radius in closed models

Partial consistency between GR and teleparallel results

Results are independent of teleparallel coupling constant

Abstract

This paper is devoted to the evaluation of the energy-momentum density components for the Friedmann models. For this purpose, we have used M${\o}$ller's pseudotensor prescription in General Relativity and a certain energy-momentum density developed from his teleparallel formulation. It is shown that the energy density of the closed Friedmann universe vanishes on the spherical shell at the radius $\rho=2\sqrt{3}$. This coincides with the earlier results available in the literature. We also discuss the energy of the flat and open models. A comparison shows a partial consistency between the M${\o}$ller's pseudotensor for General Relativity and teleparallel theory. Further, it is shown that the results are independent of the free dimensionless coupling constant of the teleparallel gravity.