Hamilton-Jacobi approach to pre-big bang cosmology and the problem of initial conditions

TL;DR

This paper applies the Hamilton-Jacobi method to string cosmology, analyzing inhomogeneity effects near the big bang singularity and their implications for initial conditions in pre-big bang models.

Contribution

It provides a second-order solution for the dilaton and metric in string cosmology using the Hamilton-Jacobi approach, highlighting inhomogeneity effects near the singularity.

Findings

Corrections from seed metric inhomogeneities are suppressed near the singularity.

Dilaton inhomogeneity corrections grow near the singularity and are suppressed in the past.

Initial metric inhomogeneities may influence pre-big bang superinflation.

Abstract

The Hamilton-Jacobi equation for the string cosmology is solved using the gradient expansion method. The zeroth order solution is taken to be the standard pre-big bang model and the second order solution is found for the dilaton and the three-metric. It indicates that corrections generated by inhomogeneities of the seed metric are suppressed near the singularity and are growing towards the asymptotic past, but corrections generated by the dilaton inhomogeneities are growing near the singularity and are suppressed in the past. Possible influences of initial metric inhomogeneities on the pre-big bang superinflation are discussed.