Past-completeness of inflationary spacetimes

Journal Article · 12 February 2023 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.107.044024 · OSTI ID:1957827

Lesnefsky, J. E.  ^[1]; Easson, D. A.  ^[2]; Davies, Paul C. W. ^[2]

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1. Arizona State Univ., Tempe, AZ (United States); Arizona State University
2. Arizona State Univ., Tempe, AZ (United States)

Here, 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 (semiclassical) cosmological concerns over physically reasonable scale factors.

• Research Organization: Arizona State Univ., Tempe, AZ (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); Foundational Questions Institute
• Grant/Contract Number: SC0019470
• OSTI ID: 1957827
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 4 Vol. 107; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English