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On the past-completeness of inflationary spacetimes

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arxiv 2207.00955 v2 pith:I4I2JRQ3 submitted 2022-07-03 gr-qc hep-th

J. E. Lesnefsky , D. A. Easson , P. C. W. Davies This is my paper · ORCID
classification gr-qchep-th
keywords cosmologicalinflationaryspacetimescompletedefinitiondiscussgeodesicgeodesically
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Obstructions to Minimal Regular Black Hole Cosmologies

    gr-qc 2026-06 conditional novelty 7.0 of 10

    Obstructions from matching conditions and completeness theorems prevent minimal regular black hole models from hosting unbounded FRW daughter cosmologies.

  2. The BGV Theorem and the Null Convergence Condition

    gr-qc 2026-07 accept novelty 6.0 of 10

    NCC plus ³R≤0 imply BGV for shear-free geodesic orthogonal foliations, but shear and non-geodesic threading make the BGV expansion directional and can evade that guarantee.

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