Abstract
Bouncing non-singular isotropic cosmological solutions are investigated in a simple model of scalar-tensor gravity. New families of such solutions are found and their properties are presented and analyzedusing an effective potential as the main tool.Bouncing solutions are shown to exist for a Higgs-like self-interactionpotential which is bounded from below, in contrast to previous solutions that appeared in the literature based on potentials which were unbounded from below. In the simplest version of a scalar field with the quartic potential and conformal coupling to gravity, bouncing spatially flat solutions either have the Hubble function diverging in the past beforethe bounce, but with a well-behaved future, or are globally regular but unstable with respect to anisotropic or inhomogeneousperturbations at some finite values of the scalar field and curvature. Regular solutions can only exist in the part of the parameter space where the maximum ofthe effective potential is larger than the first zero of the potential, and gravity becomesrepulsive at the bounce.
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