Relic Gravitational Wave And Positive Definite And Expression Of Their Energy-Momentum Pseudo-Tensor In De Sitter Background Spacetime Of The Curve

General Relativity has been published by Einstein in 1916, and the theoretics has predicted the existence of Gravitational Waves (GWS). So for, there were not find direct consequence of the detection of GWS in experimental test, in the case both experimental test and further theoretical investigation (including study of the expression of the energy-momentum pseudo-tensor for relic GWS ) become urgently necessary.In this paper, introducing that the primary background, the trend and current instance of detection of gravitational waves, and the mechanism of gravitational wave generated and the discovery of the cosmic microwave background (CMB) radiation in the universe. Now, if relic GWS were existed, one have interested are that relic GWS from cosmic big bang by detect in CMB.In particular, discuss that positive definite and energy density of static state sphere symmetry of gravitational field and energy-momentum pseudo-tensor of relic gravitational wave of both the polarized states in de sitter space-time of the curve. We use Einstien-Tolman expression of the energy-momentum pseudo tensor (EMPT) in the sphere and Cartesian coordinates, calculated the energy density of static sphere symmetry of gravitational field. It is found that energy density of static sphere symmetry of gravitational field is negative in the sphere coordinates and their energy density is positive definite in the Cartesian coordinates. This result shows that Einstien-Tolman expression of the energy-momentum pseudo tensor (EMPT) in the Cartesian coordinates have reasonable property. We calculate the energy-momentum pseudo-tensor of relic gravitational wave of both the polarized states by Riazuelo-Uzan (R-U) expression of the energy-momentum pseudo tensor (EMPT) in the Cartesian coordinates, we can see that energy density and momentum densities of relic GWs are dependent on cosmic scale factor and square of the amplitudes,. At the same time, the energy density of relic GWs is positive definite, the momentum densities components have reasonable physical behavior,and their values are independent on the directions. This result shows that the energy and momentum of relic GWs are homogeneous and isotropic. We further discuss high frequency relic GWs, and relic GWs may regard as plane GWs in high frequency. However, some physical behavior of the momentum density of relic GWs is not clear yet and it has more complex property than that of the energy density of the relic GWs, we will study these issues elsewhere. Such results...