On the possibility of a maximum fundamental density and the elimination of gravitational singularities

Abstract

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.Comment: 5 pages, 2 figures. Replaced since the Abstract is updated and further references are included. There are also some minor changes in the tex