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Lessons for quantum cosmology from anti–de Sitter black holes

Alice Di Tucci, Michal P. Heller, and Jean-Luc Lehners
Phys. Rev. D 102, 086011 – Published 13 October 2020

Abstract

Gravitational physics is arguably better understood in the presence of a negative cosmological constant than a positive one, yet there exist strong technical similarities between the two settings. These similarities can be exploited to enhance our understanding of the more speculative realm of quantum cosmology, building on robust results regarding anti–de Sitter black holes describing the thermodynamics of holographic quantum field theories. To this end, we study four-dimensional gravitational path integrals in the presence of a negative cosmological constant and with minisuperspace metrics. We put a special emphasis on boundary conditions and integration contours. The Hawking-Page transition is recovered, and we find that below the minimum temperature required for the existence of black holes the corresponding saddle points become complex. When the asymptotic anti–de Sitter space is cut off at a finite distance, additional saddle points contribute to the partition function, albeit in a very suppressed manner. These findings have direct consequences for the no-boundary proposal in cosmology, because the anti–de Sitter calculation can be brought into one-to-one correspondence with a path integral for de Sitter space with Neumann conditions imposed at the nucleation of the Universe. Our results lend support to recent implementations of the no-boundary proposal focusing on momentum conditions at the “big bang.”

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  • Received 11 August 2020
  • Accepted 25 September 2020

DOI:https://doi.org/10.1103/PhysRevD.102.086011

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Alice Di Tucci*, Michal P. Heller, and Jean-Luc Lehners

  • Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam, Germany

  • *alice.di-tucci@aei.mpg.de
  • mheller@aei.mpg.de; On leave from National Centre for Nuclear Research, 02-093 Warsaw, Poland.
  • jlehners@aei.mpg.de

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Issue

Vol. 102, Iss. 8 — 15 October 2020

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