Stable Exact Solutions in Cosmological Models with Two Scalar Fields

TL;DR

This paper investigates the stability of isotropic cosmological solutions with two scalar fields, establishing conditions for Lyapunov stability in both isotropic and anisotropic metrics, and constructs stable solutions using the superpotential method.

Contribution

It introduces new sufficient conditions for Lyapunov stability of two-field cosmological models and applies the superpotential method to construct and analyze stable kink-type solutions.

Findings

Lyapunov stability conditions are extended to anisotropic perturbations.

Stable kink-type solutions are constructed using the superpotential method.

Stability analysis includes string field theory inspired models.

Abstract

The stability of isotropic cosmological solutions for two-field models in the Bianchi I metric is considered. We prove that the sufficient conditions for the Lyapunov stability in the Friedmann-Robertson-Walker metric provide the stability with respect to anisotropic perturbations in the Bianchi I metric and with respect to the cold dark matter energy density fluctuations. Sufficient conditions for the Lyapunov stability of the isotropic fixed points of the system of the Einstein equations have been found. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for string field theory inspired cosmological models.