The holography hypothesis in pre-big-bang cosmology with string sources

The holographic ratio in Pre-big bang string cosmology is obtained in thepresence string sources. An iterative procedure is adopted to solve theequations of motion and derive the ratio in four dimensional world. First thezeroth order ratio is computed in the remote past, i.e. at $t=-\infty$, thenthe holographic ratio is obtained taking into account the evolution of thebackgrounds following the iterative procedure. The corrections to the zerothorder value of the ratio depends on the form of the initial number distributionof the strings chosen. Moreover, we estimate the holographic ratio in therecent past (i.e. when $\gamma=-\frac{1}{d}$) and in the remote past (i.e. when$\gamma= 0$), $\gamma\equiv\frac{p}{\varrho}$, in different dimensions in theEinstein frame and in the string frame. We find that in the first case it hassimilar time dependences in both the frames, especially in four dimensions theratio is explicitly computed to be the same in the two cases, whereas for$\gamma=0$ case the time dependence is different.Comment: 33 pages, latex, five figure