Geodesic Completeness in General Cosmological Scenarios
General Relativity and Quantum Cosmology
2026-04-23 v1 Cosmology and Nongalactic Astrophysics
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.
Keywords
Cite
@article{arxiv.2604.20809,
title = {Geodesic Completeness in General Cosmological Scenarios},
author = {William H. Kinney},
journal= {arXiv preprint arXiv:2604.20809},
year = {2026}
}
Comments
8 pages, 1 figure. To appear in the proceedings of Recontres de Moriond 2026