High-Frequency Gravitational Wave Propagating Through The Vacuum Robertson-Walker Spacetime And Its Energy-Momentum Pseudo-tensor

At present, the physical behavior of the high frequency gravitational waves (HFGW) propagating through the curved space-time has been studied in different cosmological models under the action of different fields and matters. However, the researches on the physical behavior of the HFGW propagating through the vacuum Robertson-Walker (R-W) spacetime are not more, especially the researches on the dynamical back-reaction of HFGW on background space-time. Thus, in the paper, it is studied the physical behavior of the HFGW in the vacuum R-W universe.Firstly, the Einstein gravitational theory is reviewed and the gravitationally radiative theory is introduced. In particular, current theoretical researches on the HFGW and are presented. Then the history of the detection of gravitational waves and some laser interferometer gravitational wave detectors are introduced particularly. Additionally, some experimental researches on the detection of the HFGW are also recommended.Based on the Einstein field equation, and then taking account of the second order perturbation of the metric and rewriting Einstein field equation, one can obtain the propagation of the HFGW in the vacuum Robertson-Walker universe and its energy momentum pseudo-tensor (EMPT) by taking the second order perturbation of the Einstein field equation as a new source of curving the space-time. By defing the EMPT of the HFGW as the value of taking Brill-Harlte average on the second order perturbation of the Einstein tensor over several wavelengths, it is found that the energy density of the HFGW under this definition of EMPT is positive definite; Moreover, this is equivalent to the value of the EMPT of the Landau-Lifshitz form which is taken the same Brill-Harlte average over several wavelengths. At the same time, the propagating equations of the HFGW in the curved space-time are obtained. It is found that, in homogenous and isotropic universe, the propagating equation is different from the one in the plane space-time and the wave front of HFGW is not plane gravitational waves. At the same time, it is pointed that some conclusions other authors obtained concerning the propagating equation is obvious. When taking the second order non-linear effects of the gravitational waves and rewriting the EMPT of HFGW as the form of perfect liquid and decomposing the"new field equation as component form, then the back-reaction of the HFGW on the background space-time is obtained. From the dynamical back-reaction equations, it is easily to find that the energy density and momentum density of HFGW will change the time evolution of scalar factor of the background space-time.