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.
