The holography hypothesis in pre-Big-Bang cosmology with string sources

The holographic ratio in pre-Big Bang string cosmology is obtained in the p resence string sources. An iterative procedure is adopted to solve the equa tions of motion and derive the ratio in four dimensional world. First the z eroth order ratio is computed in the remote past, i.e. at t = -infinity, th en the holographic ratio is obtained taking into account the evolution of t he backgrounds following the iterative procedure. The corrections to the ze roth order value of the ratio depends on the form of the initial number dis tribution of the strings chosen. Moreover, we estimate the holographic rati o in the recent past (i.e. when gamma = -1/d)and in the remote past (i.e. w hen gamma = 0), gamma equivalent to p/rho, in different dimensions in the E instein frame and in the string frame. We find that in the first case it ha s similar time dependences in both the frames, especially in four dimension s the ratio is explicitly computed to be the same in the two cases, whereas for = 0 case the time dependence is different.