Energy in an Expanding Universe in the Teleparallel Geometry

TL;DR

This paper verifies the consistency of energy-momentum and angular momentum tensors in Teleparallel Gravity, computes total energy and angular momentum in a closed FLRW universe, and derives Friedmann equations within TEGR framework.

Contribution

It explicitly verifies the energy-momentum tensor in TEGR and derives Friedmann equations, providing a consistent energy description in an expanding universe.

Findings

Total energy and angular momentum computed for closed FLRW universe.

Derived teleparallel Friedmann equations equivalent to GR.

Compared energy results with Einstein and Landau-Lifshitz pseudotensors.

Abstract

The main purpose of this paper is to explicitly verify the consistency of the energy-momentum and angular momentum tensor of the gravitational field established in the Hamiltonian structure of the Teleparallel Equivalent of General Relativity (TEGR). In order to reach these objectives, we obtained the total energy and angular momentum (matter plus gravitational field) of the closed universe of the Friedmann-Lemaitre-Robertson-Walker (FLRW). The result is compared with those obtained from the pseudotensors of Einstein and Landau-Lifshitz. We also applied the field equations (TEGR) in an expanding FLRW universe. Considering the stress energy-momentum tensor for a perfect fluid, we found a teleparallel equivalent of Friedmann equations of General Relativity (GR).