Cyclic Cosmology and Geodesic Completeness

TL;DR

This paper examines cyclic cosmological models with periodic Hubble parameters and growing scale factors, demonstrating that entropy dissipation mechanisms lead to geodesic past-incompleteness, challenging their true cyclicity.

Contribution

It proves that bouncing universes relying on scale factor growth for entropy dissipation are necessarily geodesically past-incomplete, refuting their potential for true cyclicity.

Findings

Bouncing models with entropy shedding are geodesically past-incomplete.

Growth of the scale factor cannot produce a truly cyclic universe.

Such models cannot be extended infinitely into the past.

Abstract

We consider recently proposed bouncing cosmological models for which the Hubble parameter is periodic in time, but the scale factor grows from one cycle to the next as a mechanism for shedding entropy. Since the scale factor for a flat universe is equivalent to an overall conformal factor, it has been argued that this growth corresponds to a physically irrelevant rescaling, and such bouncing universes can be made perfectly cyclic, extending infinitely into the past and future. We show that any bouncing universe which uses growth of the scale factor to dissipate entropy must necessarily be geodesically past-incomplete, and therefore cannot be truly cyclic in time.