The Holography Hypothesis in Pre-Big-Bang Cosmology with String Sources

TL;DR

This paper investigates the holographic ratio in pre-big bang string cosmology with string sources, using an iterative method to analyze its evolution and dependence on initial conditions across different dimensions and frames.

Contribution

It introduces an iterative approach to compute the holographic ratio in pre-big bang cosmology, accounting for string sources and background evolution in various dimensions and frames.

Findings

Holographic ratio computed at different cosmological times and conditions.

Time dependence of the ratio is similar in both frames for certain parameters.

Explicit ratio calculation in four dimensions shows frame independence in specific cases.

Abstract

The holographic ratio in Pre-big bang string cosmology is obtained in the presence string sources. An iterative procedure is adopted to solve the equations of motion and derive the ratio in four dimensional world. First the zeroth order ratio is computed in the remote past, i.e. at $t=-\infty$, then the holographic ratio is obtained taking into account the evolution of the backgrounds following the iterative procedure. The corrections to the zeroth order value of the ratio depends on the form of the initial number distribution of the strings chosen. Moreover, we estimate the holographic ratio in the recent 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 the Einstein frame and in the string frame. We find that in the first case it has similar time dependences in both the frames, especially in four dimensions the ratio is explicitly computed to be the same in the two cases, whereas for $\gamma=0$ case the time dependence is different.