Stability properties and asymptotics for N non-minimally coupled scalar fields cosmology

TL;DR

This paper studies the stability and long-term behavior of cosmological models with multiple non-minimally coupled scalar fields, showing that chaos is unlikely and solutions tend to de Sitter or Minkowski states.

Contribution

It generalizes previous results from one and two scalar fields to models with N interacting fields, establishing stability and asymptotic properties.

Findings

Lyapunov function construction indicates absence of chaos.

Solutions tend to de Sitter or Minkowski fixed points.

Universe approaches matter-dominated era at large times.

Abstract

We consider here the dynamics of some homogeneous and isotropic cosmological models with $N$ interacting classical scalar fields non-minimally coupled to the spacetime curvature, as an attempt to generalize some recent results obtained for one and two scalar fields. We show that a Lyapunov function can be constructed under certain conditions for a large class of models, suggesting that chaotic behavior is ruled out for them. Typical solutions tend generically to the empty de Sitter (or Minkowski) fixed points, and the previous asymptotic results obtained for the one field model remain valid. In particular, we confirm that, for large times and a vanishing cosmological constant, even in the presence of the extra scalar fields, the universe tends to an infinite diluted matter dominated era.