On the energy of homogeneous cosmologies

TL;DR

This paper introduces a method to calculate the energy of homogeneous cosmological models within a broad class of gravity theories, revealing that energy vanishes for class A models but is negative for class B models, including teleparallel theories.

Contribution

It provides a unified prescription for computing energy in homogeneous cosmologies across various tetrad-based gravity theories, extending previous results.

Findings

Energy vanishes for all Bianchi class A models.

Energy does not vanish and is negative for all Bianchi class B models.

The results hold across a three-parameter family of tetrad-teleparallel theories.

Abstract

An energy for the homogeneous cosmological models is presented. More specifically, using an appropriate natural prescription, we find the energy within any region with any gravitational source for a large class of gravity theories--namely those with a tetrad description--for all 9 Bianchi types. Our energy is given by the value of the Hamiltonian with homogeneous boundary conditions; this value vanishes for all regions in all Bianchi class A models, and it does not vanish for any class B model. This is so not only for Einstein's general relativity but, moreover, for the whole 3-parameter class of tetrad-teleparallel theories. For the physically favored one parameter subclass, which includes the teleparallel equivalent of Einstein's theory as an important special case, the energy for all class B models is, contrary to expectation, negative.