Scalar-field cosmologies with an arbitrary potential

TL;DR

This paper analyzes the long-term behavior of flat and negatively curved FRW cosmological models with scalar fields and arbitrary non-negative potentials, showing they generally expand forever and detailing conditions for scalar field asymptotics.

Contribution

It provides a dynamical systems proof that most such cosmologies expand forever and explores conditions for scalar fields to approach potential minima.

Findings

Most models expand forever.

Energy density tends to zero asymptotically.

Conditions identified for scalar field to reach potential minima.

Abstract

We study the late time evolution of flat and negatively curved FRW models with a perfect fluid matter source and a scalar field having an arbitrary non-negative potential function $V(\phi) .$ We prove using a dynamical systems approach four general results for a large class of non-negative potentials which show that almost always the universe ever expands. In particular, for potentials having a local zero minimum, flat and negatively curved FRW models are ever expanding and the energy density asymptotically approaches zero. We investigate the conditions under which the scalar field asymptotically approaches the minimum of the potential. We discuss the question of whether a closed FRW with ordinary matter can avoid recollapse due to the presence of a scalar field with a non-negative potential.