Stochastic Gravitational Wave Background in Brane World Cosmology

We investigate the cosmological evolution of gravitational waves in Friedman-Robertson-Walker brane world models embedded in a five dimensional anti de-Sitter spacetime. To predict the spectrum of stochastic gravitational background at present generated in the inflationary phase, we numerically calculate the evolution of gravitational waves according to the method developed in our previous paper [K. Ichiki and K. Nakamura, arXiv:hep-th/0310282]. The resulting logarithmic energy spectrum is significantly altered from that of the standard four dimensional inflationary models in the frequency range f > f_{AdS} ~ 10^{-4} Hz, which corresponds to the curvature scale we set of anti de-Sitter spacetime, $l ~ 1$mm.