Negative potentials and collapsing universes

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 −∞ in a finite time. This finite-time singularity theorem is true for the arbitrary coupling coefficient, provided that it is a bounded function of the scalar field.