The energy of Bianchi type I and II universes in teleparallel gravity

Abstract

For certain models, the energy of the universe, which includes the energy of both matter and the gravitational fields, is obtained by using the quasi-local energy-momentum in teleparallel gravity. It is shown that, in the case of the Bianchi type I and II universes, not only the total energy but also the quasi-local energy-momentum for any region vanishes independently of the three dimensionless coupling constants of teleparallel gravity.