  With this note we want to point out that already in the early days of
cosmology it was understood that negative pressure could eliminate
gravitational singularities in a natural way e.g. E.B. Gliner, Sov. Phys. JETP
22(1966)378 and M.A. Markov, Pis'ma Zh. Eksp. Teor. Fiz. 36, No 6, 214-216 (20
Sept. 1982). Today, with the discovery of dark energy and the strong evidence
in favor of an inflationary start of the Big Bang, the existence of negative
pressure is widely accepted. In fundamental physics, phase transitions are
generally thought to be reversible (Cf. Ellis, New Astronomy Reviews Volume 46,
Issue 11, October 2002, P. 645). It seems likely then that if inflation has
occurred, the process should be reversible. I.e. when the increasing density in
a collapsing universe or star reaches a certain limit it should go through a
phase transition to a medium with an equation of state of the type $p=\omega
\rho$, where $-1< \omega <-1/3$. If this phase transition is fundamental, i.e.
occurs for all energy densities, a collapse will always reach a minimum radius
and bounce. If the phase transition is symmetric, the result will lead to
oscillating universes. If however the phase transition is associated with an
hysteresis effect, a collapsing star may, succeeding the bounce inflate into a
new universe with a subsequent phase transition becomes dominated by ordinary
relativistic matter. The aim of this note is study the time development of a
model which mimics this process.
