A dynamical system analysis of bouncing cosmology with spatial curvature

TL;DR

This paper analyzes a bouncing cosmological model with spatial curvature using dynamical systems theory, identifying conditions for bounce scenarios and stability of critical points.

Contribution

It introduces a dynamical system approach to analyze bouncing cosmology with spatial curvature, including stability analysis and critical points at infinity.

Findings

Bouncing occurs near points at infinity on the Poincare sphere.

Critical points at infinity can be saddle or saddle-node, enabling bounce scenarios.

Stability analysis provides insights into the evolution of curved cosmological models.

Abstract

The present work deals with a FLRW cosmological model with spatial curvature and minimally coupled scalar field as the matter content. The curvature term behaves as a perfect fluid with the equation of state parameter w_K = -1/3 Using suitable transformation of variables, the evolution equations are reduced to an autonomous system for both power law and exponential form of the scalar potential. The critical points are analyzed with center manifold theory and stability has been discussed. Also, critical points at infinity have been studied using the notion of Poincare sphere. Finally, the cosmological implications of the critical points and cosmological bouncing scenarios are discussed. It is found that the cosmological bounce takes place near the points at infinity when the non-isolated critical points on the equator of the Poincare sphere are saddle or saddle-node in nature.