• DOI:10.1103/PhysRevD.107.044024
• Corpus ID: 250264825

Past-completeness of inflationary spacetimes

@article{Lesnefsky2022PastcompletenessOI,
  title={Past-completeness of inflationary spacetimes},
  author={Joseph Lesnefsky and Damien A Easson and Paul C. W. Davies},
  journal={Physical Review D},
  year={2022}
}

• J. Lesnefsky, D. Easson, P. Davies
• Published 3 July 2022
• Mathematics
• Physical Review D

We discuss the question of whether or not inflationary spacetimes can be geodesically complete in the infinite past. Geodesic completeness is a necessary condition for averting an initial singularity during eternal inflation. It is frequently argued that cosmological models which are expanding sufficiently fast (having average Hubble expansion rate $H_{avg}>0$) must be incomplete in null and timelike past directions. This well-known conjecture relies on specific bounds on the integral of the Hubble parameter over a past-directed timelike or null geodesic. As stated, we show this claim is an open issue. We show that the calculation of $H_{avg}$ yields a continuum of results for a given spacetime predicated upon the underlying topological assumptions. We present an improved definition for $H_{avg}$ and introduce an uncountably infinite cohort of cosmological solutions which are geodesically complete despite having $H_{avg}>0$. We discuss a standardized definition for inflationary spacetimes as well as quantum (semi-classical) cosmological concerns over physically reasonable scale factors.