  Recent data suggest that the Universe could be positively curved. Combined
with an inflationary stage, this might lead to a curvature bounce instead of
the Big Bang. The background evolution is presented, as a function of the
parameters controlling the cosmic evolution. The primordial tensor spectrum is
also calculated and possible observational footprints of the model are
underlined. Several potentials are considered and general remarks are made
about "naturalness" in this context.
