Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound

TL;DR

This paper proves that scalar fields with potentials having a positive lower bound can cause accelerated expansion in homogeneous cosmological models, extending Wald's theorem to a broader class of potentials and analyzing late-time behavior.

Contribution

It generalizes Wald's theorem to scalar fields with positive lower bound potentials and provides detailed late-time asymptotic analysis.

Findings

Scalar fields with positive lower bound potentials lead to accelerated expansion.

Extended Wald's theorem to a wider class of potentials.

Detailed late-time asymptotic behavior characterized.

Abstract

In many cases a nonlinear scalar field with potential $V$ can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for homogeneous spacetimes. It is shown that, under the assumption that $V$ has a strictly positive minimum, Wald's theorem on spacetimes with positive cosmological constant can be generalized to a wide class of potentials. In some cases detailed information on late-time asymptotics is obtained. Results on the behaviour in the past time direction are also presented.