Negative potentials and collapsing universes

Abstract

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.

11 pages, 1 figure

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Cited by in corpus (6)

• Possible evolution of a bouncing universe in cosmological models with non-minimally coupled scalar fields
• Generalized scalar field cosmologies: theorems on asymptotic behavior
• Scalar-Tensor Quintessence with a linear potential: Avoiding the Big Crunch cosmic doomsday
• Global models of collapsing scalar field: endstate
• Gravitational collapse of a spherical scalar field
• Integrable cosmological models with non-minimal coupling and bounce solutions