Negative potentials and collapsing universes II

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.