Negative potentials and collapsing universes II

Abstract

Completing a previous analysis started in Giambò et al (2015 Class. Quantum Grav. 32 035009 ), we study flat Friedmann–Lemaître–Robertson–Walker 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 − ∞ 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.