Cosmological milestones and energy conditions

TL;DR

This paper classifies various cosmological milestones, including singularities and bounces, using kinematic and dynamical methods, and explores their relation to energy conditions in a highly general, model-independent framework.

Contribution

It provides an extensive, generalized classification of cosmological events and their relation to energy conditions, expanding beyond traditional singularities.

Findings

Classified cosmological milestones using power series expansions.

Connected scale-factor singularities to curvature singularities.

Derived model-independent constraints on energy conditions at milestones.

Abstract

Until recently, 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 talk, we present an extensive 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. Since the classification is extremely general, and modulo certain technical assumptions complete, the corresponding results are to a high degree model-independent.