Certain aspects of regularity in scalar field cosmological dynamics

TL;DR

This paper investigates the dynamics of scalar field cosmology in FRW universes, revealing persistent zones of regular motion and islands of stability through geometric and numerical analysis.

Contribution

It introduces a geometric approach using Maupertuis principle to identify regular regions in scalar field cosmological models, including beyond the physical domain.

Findings

Zones of positive curvature exist for all considered potentials.

Numerical evidence of islands of regular motion in shallow potentials.

Regular islands also found beyond the physical domain for quadratic potentials.

Abstract

We consider dynamics of the FRW Universe with a scalar field. Using Maupertuis principle we find a curvature of geodesics flow and show that zones of positive curvature exist for all considered types of scalar field potential. Usually, phase space of systems with the positive curvature contains islands of regular motion. We find these islands numerically for shallow scalar field potentials. It is shown also that beyond the physical domain the islands of regularity exist for quadratic potentials as well.