  We consider gravity theory with varying speed of light and varying
gravitational constant. Both constants are represented by non-minimally coupled
scalar fields. We examine the cosmological evolution in the near curvature
singularity regime. We find that at the curvature singularity the speed of
light goes to infinity while the gravitational constant vanishes. This
corresponds to the Newton's Mechanics limit represented by one of the vertex of
the Bronshtein-Zelmanov-Okun cube. The cosmological evolution includes both the
pre-big-bang and post-big-bang phases separated by the curvature singularity.
We also investigate the quantum counterpart of the considered theory and find
the probability of transition of the universe from the collapsing pre-big-bang
phase to the expanding post-big-bang phase.
