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arXiv · 2207.00955

On the past-completeness of inflationary spacetimes

J. E. Lesnefsky·D. A. Easson·P. C. W. Davies
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Abstract

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.

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J. E. Lesnefsky, D. A. Easson, P. C. W. Davies. 2022-07-03. On the past-completeness of inflationary spacetimes. https://doi.org/10.1103/physrevd.107.044024

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