2 6 O ct 1 99 9 Hamilton - Jacobi approach to pre - big bang cosmology and the problem of initial conditions

The Hamilton-Jacobi equation for the low energy string effective action is solved using the gradient expansion method. The field equations are also expanded by the number of spatial gradients and the second order solution is found for the three-metric. The second order solution allows us to study the influence of initial inhomogeneities to the duration of pre-big bang superinflation. We conclude that the initial inhomogeneities become negligible during the superinflation, but the initial patch has to be extremely flat and homogeneous to get the sufficient amount of inflation. 1 Electronic address: [email protected] 2 Electronic address: [email protected]