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With the recent claim that gravitational waves were finally detected [1 and 2] and with other efforts around the world for GWs detection [3, 4, 5 and 6], its is reasonable to imagine that the relic gravitational wave background could be detected in some time in the future and with such information gather some hints about the origin of the universe. But, it ́s also be considered that gravity has self-interaction, with such assumption it ́s reasonable to expect that these gravitatinal wave will interact with the relic or non-relic GW background by scattering, for example. Such interaction should decresase the distance which such propagating waves could be detected The propagation of gravitational waves (GWs) is analysed in an asymptotically de Sitter space by the perturbation expansion around Minkowski. The stochastic relic GW background is given by a dimensionless function of the frequency [7 and 8]. Another way to characterize such background could be seem in [9 and 10]. Using the case of de Sitter inflationary phase scenario [7, 8 and 10], the perturbation propagates through a FRW background with a metric

Gravitational Waves Propagation through the Stochastic Background of Gravitational Waves