  We propose a gravitational model with a Brans-Dicke-type scalar field having,
in the would-be action, a "wrong-sign" kinetic term and a quartic interaction
term. In a cosmological context, we obtain, depending on the boundary
conditions, either the Friedmann solution or a kink-bounce solution. The
expanding-universe Friedmann solution has a big bang curvature singularity,
whereas the kink-bounce solution has a nonsingular bouncing behavior of the
cosmic scale factor. The bounce occurs precisely at the moment when the scalar
field of the kink-type configuration goes through zero, making for a vanishing
effective gravitational coupling.
