  The aim of this paper is to show, that the 'oscillating universe' is a viable
alternative to inflation. We remind that this model provides a natural solution
to the flatness or entropy and to the horizon problem of standard cosmology. We
study the evolution of density perturbations and determine the power spectrum
in a closed universe. The results lead to constraints of how a previous cycle
might have looked like. We argue that most of the radiation entropy of the
present universe may have originated from gravitational entropy produced in a
previous cycle.
  We show that measurements of the power spectrum on very large scales could in
principle decide whether our universe is closed, flat or open.
