The total energy-momentum of the universe in teleparallel gravity

TL;DR

This paper explores the conservation of total energy-momentum in teleparallel gravity, demonstrating that the universe's total energy-momentum vanishes regardless of curvature or coupling constants, using Noether's theorem.

Contribution

It provides a detailed analysis of energy-momentum conservation in teleparallel gravity and shows the total energy-momentum of the universe is zero, independent of specific parameters.

Findings

Total energy-momentum vanishes for the universe in teleparallel gravity.

Energy-momentum current has a superpotential, ensuring conservation.

Result holds regardless of curvature parameter and coupling constants.

Abstract

We investigate the conservation law of energy-momentum in teleparallel gravity by using general Noether theorem. The energy-momentum current has also superpotential and is therefore identically conserved. The total energy-momentum, which includes the contributions of both matter and gravitational fields, is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. As an example, the universe in teleparallel gravity is investigated. It is shown that the total energy-momentum vanishes independently of both the curvature parameter and the three dimensionless coupling constants of teleparallel gravity.