Intermediate inflation and the slow-roll approximation

TL;DR

This paper demonstrates that certain scalar field potentials lead to accelerated cosmic expansion, extending Wald's theorem to a broader class of potentials satisfying slow-roll conditions.

Contribution

It generalizes Wald's theorem by showing that a wide class of positive, vanishing-at-infinity potentials induce late-time acceleration under slow-roll restrictions.

Findings

Spatially homogeneous solutions exhibit late-time acceleration.

Potentials satisfying specific slow-roll conditions lead to accelerated expansion.

Results extend Wald's theorem to new classes of scalar field potentials.

Abstract

It is shown that spatially homogeneous solutions of the Einstein equations coupled to a nonlinear scalar field and other matter exhibit accelerated expansion at late times for a wide variety of potentials $V$. These potentials are strictly positive but tend to zero at infinity. They satisfy restrictions on $V'/V$ and $V''/V'$ related to the slow-roll approximation. These results generalize Wald's theorem for spacetimes with positive cosmological constant to those with accelerated expansion driven by potentials belonging to a large class.