Bouncing Cosmological Isotropic Solutions in Scalar-Tensor Gravity
  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 analyzed using an effective potential as
the main tool. Bouncing solutions are shown to exist for a Higgs-like
self-interaction potential 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 before the
bounce, but with a well-behaved future, or are globally regular but unstable
with respect to anisotropic or inhomogeneous perturbations 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 of the effective potential is
larger than the first zero of the potential, and gravity becomes repulsive at
the bounce.
