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 .