Hamilton-Jacobi Approach to Pre-Big Bang Cosmology at Long-wavelengths

TL;DR

This paper applies Hamilton-Jacobi theory to low-energy string cosmology, deriving invariant solutions under scale factor duality and connecting them with the Lagrangian formalism, providing insights into pre-Big Bang models.

Contribution

It introduces a Hamilton-Jacobi framework for string cosmology that explicitly maintains scale factor duality and simplifies the momentum constraints.

Findings

Derived the general solution to the Hamilton-Jacobi equation for string cosmology.

Showed the solution reduces to quasi-isotropic form when gravitational evolution is neglected.

Expressed duality transformations as coordinate changes in field space.

Abstract

We apply the long-wavelength approximation to the low energy effective string action in the context of Hamilton-Jacobi theory. The Hamilton-Jacobi equation for the effective string action is explicitly invariant under scale factor duality. We present the leading order, general solution of the Hamilton-Jacobi equation. The Hamilton-Jacobi approach yields a solution consistent with the Lagrange formalism. The momentum constraints take an elegant, simple form. Furthermore this general solution reduces to the quasi-isotropic one, if the evolution of the gravitational field is neglected. Duality transformation for the general solution is written as a coordinate transformation in an abstract field space.