Geodesic Completeness in General Cosmological Scenarios

TL;DR

This paper discusses the extension of the Borde-Guth-Vilenkin theorem to various cosmological models, demonstrating that certain cyclic models are also geodesically incomplete, implying the need for a boundary or initial condition.

Contribution

It generalizes the BGV theorem to inhomogeneous and cyclic cosmologies and applies it to show the geodesic incompleteness of a specific cyclic model.

Findings

Cyclic model by Ijjas and Steinhardt is geodesically incomplete.

The BGV theorem can be extended beyond inflationary spacetimes.

Inhomogeneous and cyclic models may require boundary conditions due to geodesic incompleteness.

Abstract

The well-known Borde-Guth-Vilenkin Theorem shows that inflationary spacetimes are generically geodesically past-incomplete, necessitating the existence of a pre-inflationary boundary of some sort, possibly singular. I discuss the generalization of the BGV theorem to spacetimes beyond inflation, including inhomogeneous and cyclic models. As an example, I show that the cyclic model proposed by Ijjas and Steinhardt is geodesically incomplete.