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 $-\infty$ 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. 
Roberto Giamb\`o, John Miritzis and Koralia Tzanni
gr-qc