The Cosmological Models with Jump Discontinuities

TL;DR

This paper explores the often overlooked jump discontinuities in cosmological models, revealing new scenarios where such singularities can lead to finite scale factors despite diverging physical parameters, acting as phase transitions.

Contribution

It introduces the study of first-kind jump discontinuities in cosmology, demonstrating their role in novel evolution scenarios and potential as phase transitions.

Findings

Models with finite equation of state parameter despite diverging density and pressure.

Jump discontinuities in derivatives of the scale factor lead to new singularity types.

Discontinuities can enable extension of cosmological evolution beyond singularities.

Abstract

The article is dedicated to one of the most undeservedly overlooked properties of the cosmological models: the behaviour at, near and due to a jump discontinuity. It is most interesting that while the usual considerations of the cosmological dynamics deals heavily in the singularities produced by the discontinuities of the second kind (a.k.a. the essential discontinuities) of one (or more) of the physical parameters, almost no research exists to date that would turn to their natural extension/counterpart: the singularities induced by the discontinuities of the first kind (a.k.a. the jump discontinuities). It is this oversight that this article aims to amend. In fact, it demonstrates that the inclusion of such singularities allows one to produce a number of very interesting scenarios of cosmological evolution. For example, it produces the cosmological models with a finite value of the equation of state parameter $w=p/\rho$ even when both the energy density and the pressure diverge, while at the same time keeping the scale factor finite. Such a dynamics is shown to be possible only when the scale factor experiences a finite jump at some moment of time. Furthermore, if it is the first derivative of the scale factor that experiences a jump, then a whole new and different type of a sudden future singularity appears. Finally, jump discontinuities suffered by either a second or third derivatives of a scale factor lead to cosmological models experiencing a sudden dephantomization -- or avoiding the phantomization altogether. This implies that theoretically there should not be any obstacles for extending the cosmological evolution beyond the corresponding singularities; therefore, such singularities can be considered a sort of a cosmological phase transition.