Dynamics of a scalar field in Robertson-Walker spacetimes

TL;DR

This paper studies the behavior of a scalar field in curved cosmological models, identifying stable solutions and their potentials, including known cosmological solutions as special cases.

Contribution

It provides a comprehensive analysis of scalar field dynamics in curved universes, deriving fixed points and potentials, and unifying various known solutions under a general framework.

Findings

Fixed point solutions are late-time attractors.

Derived scalar potentials for stable solutions.

Unified known solutions like power law, exponential, and de-Sitter as limits.

Abstract

We analyze the dynamics of a single scalar field in Friedmann-Robertson-Walker universes with spatial curvature. We obtain the fixed point solutions which are shown to be late time attractors. In particular, we determine the corresponding scalar field potentials which correspond to these stable solutions. The analysis is quite general and incorporates expanding and contracting universes with both positive and negative scalar potentials. We demonstrate that the known power law, exponential, and de-Sitter solutions are certain limits of our general set of solutions.