Negative potentials and collapsing universes II

TL;DR

This paper analyzes flat FLRW cosmological models with a scalar field and negative potentials, showing that most evolutions lead to a finite-time collapse unless the potential has a specific flat plateau at infinity.

Contribution

It extends previous work by characterizing the conditions under which collapsing or ever-expanding universes occur with negative scalar potentials.

Findings

Hubble function diverges to -infinity in finite time for most models.

A flat plateau in the potential at zero allows for both recollapsing and expanding solutions.

Most models inevitably lead to a finite-time singularity unless specific potential conditions are met.

Abstract

Completing a previous analysis started in [1], we study flat Friedmann--Lema\^{\i}tre--Robertson--Walker (FLRW) models with a perfect fluid matter source and a scalar field nonminimally coupled to matter, self--interacting with a potential that may attain negative values. We prove that the evolution generically forces the Hubble function to diverge to $-\infty$ in a finite time, except in case the potential exhibits a flat plateau at infinity (tending to zero from below); in that case we find conditions which may give rise to ever expanding or recollapsing cosmologies.