On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

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Inflationary spacetimes have been argued to be past geodesically incomplete in many situations. However, whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended (potentially into another phase of the universe) is generally unknown. Both questions have important physical implications. In this paper, we take a closer look at the geometrical structure of inflationary spacetimes and investigate these very questions. We first classify which past inflationary histories have a scalar curvature singularity and which might be extendible and/or non-singular in homogeneous and isotropic cosmology with flat spatial sections. Then, we derive rigorous extendibility criteria of various regularity classes for quasi-de Sitter spacetimes that evolve from infinite proper time in the past. Finally, we show that beyond homogeneity and isotropy, special continuous extensions respecting the Einstein field equations with a perfect fluid must have the equation of state of a de Sitter universe asymptotically. An interpretation of our results is that past-eternal inflationary scenarios are most likely physically singular, except in situations with very special initial conditions.

TidsskriftJournal of High Energy Physics
Udgave nummer10
Antal sider64
StatusUdgivet - 2023

Bibliografisk note

Funding Information:
We thank Eric Woolgar for stimulating discussions in the initial stages of this project. We further thank the stimulating atmosphere at the Fields Institute throughout the Thematic Program on Nonsmooth Riemannian and Lorentzian Geometry and especially during the Low Regularity Physics and Geometry Seminar and the Workshop on Mathematical Relativity, Scalar Curvature and Synthetic Lorentzian Geometry. This publication was supported by the Fields Institute for Research in Mathematical Sciences. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the Institute. E. Ling was supported by Carlsberg Foundation CF21-0680 and Danmarks Grundforskningsfond CPH-GEOTOP-DNRF151. This research was also supported by a Discovery Grant from the Natural Science and Engineering Research Council of Canada (NSERC) and partly by the Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities.

Publisher Copyright:
© 2023, The Author(s).

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