Negative potentials and collapsing universes

TL;DR

This paper proves that certain cosmological models with scalar fields and matter sources inevitably encounter finite-time singularities where the universe's expansion rate diverges negatively, under specific potential and coupling conditions.

Contribution

It establishes a general finite-time singularity theorem for Friedmann-Robertson-Walker models with nonminimally coupled scalar fields and bounded potentials that tend to minus infinity.

Findings

Hubble function diverges to -infinity in finite time

Finite-time singularity occurs under specific potential conditions

Results hold for arbitrary bounded coupling functions

Abstract

We study Friedmann--Robertson--Walker models with a perfect fluid matter source and a scalar field nonminimally coupled to matter. We prove that a general class of bounded from above potentials which fall to minus infinity as the field goes to minus infinity, forces the Hubble function to diverge to $-\infty$ in a finite time. This finite-time singularity theorem is true for arbitrary coupling coefficient, provided that it is a bounded function of the scalar field.