Negative potentials and collapsing universes II

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 $-\mathrm{\infty }$ 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.