Energy--Momentum Pseudo-Tensor of Relic Gravitational Wave of Both the Polarized States

Unlike usual celestial gravitational waves, the relic gravitational waves (RGWs) form random signals in curved spacetime background. We calculate the energy--momentum pseudo-tensor of a certain component of the RGWs propagating along arbitrary directions in Cartesian coordinates. It is found that the energy density of RGWs is positive definitely, and the momentum density components have reasonable behaviour. Such results may provide a theoretical basis for the detection of RGWs.