The gravitational energy density of the Universe

Abstract

The teleparallel gravitational energy–momentum tensor density of the Friedmann–Lemaître–Robertson–Walker spacetime is calculated and analyzed: it is decomposed into density, isotropic pressure, non-isotropic pressures, and the heat-flux 4-vector; the antisymmetric part is decomposed into “electric” and “magnetic” components. It is found that the gravitational field obeys a radiation-like equation of state, the antisymmetric part does not contribute to the gravitational energy–momentum; and the total energy density, the non-isotropic pressures and the heat-flux 4-vector vanish for spatially flat universes. Finally, it is verified that the field equations have a well-defined vacuum.