Necessary and sufficient conditions for big bangs, bounces, crunches, rips, sudden singularities, and extremality events

TL;DR

This paper provides a comprehensive classification of various cosmological singularities and milestones in FRW models, establishing conditions for their occurrence and relation to energy conditions using generalized power series and Friedmann equations.

Contribution

It introduces a complete, model-independent catalogue of cosmological events with necessary and sufficient conditions, including new insights into their dynamical and kinematical properties.

Findings

Defined generalized power series for scale factor behavior

Established relations between singularities and curvature conditions

Derived conditions for energy compliance at cosmological milestones

Abstract

The physically relevant singularities occurring in FRW cosmologies had traditionally been thought to be limited to the "big bang", and possibly a "big crunch". However, over the last few years, the zoo of cosmological singularities considered in the literature has become considerably more extensive, with "big rips" and "sudden singularities" added to the mix, as well as renewed interest in non-singular cosmological events such as "bounces" and "turnarounds". In this article we present a complete catalogue of such cosmological milestones, both at the kinematical and dynamical level. First, using generalized power series, purely kinematical definitions of these cosmological events are provided in terms of the behaviour of the scale factor a(t). The notion of a "scale-factor singularity'" is defined, and its relation to curvature singularities (polynomial and differential) is explored. Second, dynamical information is extracted by using the Friedmann equations (without assuming even the existence of any equation of state) to place constraints on whether or not the classical energy conditions are satisfied at the cosmological milestones. We use these considerations to derive necessary and sufficient conditions for the existence of cosmological milestones such as bangs, bounces, crunches, rips, sudden singularities, and extremality events. Since the classification is extremely general, the corresponding results are to a high degree model-independent: In particular, we provide a complete characterization of the class of bangs, crunches, and sudden singularities for which the dominant energy condition is satisfied.