  We study homogeneous isotropic universe in a graviton-dilaton theory
obtained, in a previous paper, by a simple requirement that the theory be able
to predict non trivial values for $\beta$ and/or $\gamma$ for a charge neutral
point star, without any naked singularities. We find that in this universe the
physical time can be continued indefinitely into the past or future, and that
all the physical curvature invariants are always finite, showing the absence of
big bang singularity. Adding a dilaton potential, we find again the same
features. As a surprising bonus, there emerges naturally a Brans-Dicke
function, which has precisely the kind of behaviour needed to make $\omega_{bd}
({\rm today}) > 500$ in hyperextended inflation.
