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The physically relevant singularities occurring in FRW cosmologies hadtraditionally been thought to be limited to the "big bang", and possibly a "bigcrunch". However, over the last few years, the zoo of cosmologicalsingularities considered in the literature has become considerably moreextensive, with "big rips" and "sudden singularities" added to the mix, as wellas renewed interest in non-singular cosmological events such as "bounces" and"turnarounds".  In this article we present a complete catalogue of such cosmologicalmilestones, both at the kinematical and dynamical level. First, usinggeneralized power series, purely kinematical definitions of these cosmologicalevents are provided in terms of the behaviour of the scale factor a(t). Thenotion of a "scale-factor singularity'" is defined, and its relation tocurvature singularities (polynomial and differential) is explored. Second,dynamical information is extracted by using the Friedmann equations (withoutassuming even the existence of any equation of state) to place constraints onwhether or not the classical energy conditions are satisfied at thecosmological milestones. We use these considerations to derive necessary andsufficient conditions for the existence of cosmological milestones such asbangs, bounces, crunches, rips, sudden singularities, and extremality events.Since the classification is extremely general, the corresponding results are toa high degree model-independent: In particular, we provide a completecharacterization of the class of bangs, crunches, and sudden singularities forwhich the dominant energy condition is satisfied.Comment: 20 pages, uses iopart.cls; several references adde

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