  The generalized kinetic term of a dilaton gives the classical superinflation
without recourse to any potential, and the quantum version of the dilaton
gravity exhibits the finite curvature and graceful exit. For $p=2$ case, the
model corresponds to the RST quantization of the s-wave sector of the
four-dimensional Einstein cosmology. Further, the de Sitter universe is
realized for $p=8$ and the smooth transition to the Minkowski space-time is
possible. Even in the accelerating contraction case of the universe for
$-4<p<0$, the curvature singularity does not appear in a certain branch.
