Energy momentum pseudo-tensor of high frequency gravitational waves and their dynamical back-reaction

To describe properties of the high frequency gravitational wave (HFGW) propagating through the vacuum gravitational field in Robertson-Walker background space-time, we calculated its energy momentum pseudo-tensor (EMPT) in the limit of short wavelengths by taking the Brill-Hartle average on the second order perturbation of the Einstein tensor over several wavelengths. By rewriting the EMPT as a form of perfect fluid, the dynamical back-reaction of HFGW on the background space-time was discussed. The result shows that the energy density of HFGW, which is in the gauge we chose, is positive definite. The HFGW serves as a source for curving the background space-time and affects the dynamical evolution and time evolution of the scale factor of the Robertson-Walker metric.