Energy of homogeneous cosmologies

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 nine 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 three-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.