De Sitter space is sometimes not empty

Journal Article · 19 February 2024 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep02(2024)135 · OSTI ID:2433816

Balasubramanian, Vijay ^[1]; Nomura, Yasunori ^[2]; Ugajin, Tomonori ^[3]

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1. Univ. of Pennsylvania, Philadelphia, PA (United States); Vrije Universiteit Brussel (VUB), Brussels (Belgium); Santa Fe Inst. (SFI), Santa Fe, NM (United States)
2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), Wako (Japan); Univ. of Tokyo (Japan). Kavli Institute for the Physics and Mathematics of the Universe (WPI)
3. Kyoto Univ. (Japan)

Multiple lines of evidence suggest that the Hilbert space of an isolated de Sitter universe is one dimensional but can appear larger when probed by a gravitating observer. To test this idea, we compute the von Neumann entropy of a field theory in a two-dimensional de Sitter universe which is entangled in a thermal-like state with the same field theory on a disjoint, asymptotically anti-de Sitter (AdS) black hole. Previously, it was shown that the replica trick for computing the entropy of such entangled gravitating systems requires the inclusion of a non-perturbative effect in quantum gravity — novel wormholes connecting the two spaces. Here we show that: (a) the expected wormholes connecting de Sitter and AdS universes exist, avoiding a no-go theorem via the presence of sources on the AdS boundary; (b) the entanglement entropy vanishes if the nominal entropy of the de Sitter cosmological horizon (S_ds = $$A^{dS}_{horizon}$$/4G_N) is less than the entropy of the AdS black hole horizon (S_BH = $$A^{AdS}_{horizon}$$/4G_N), i.e., S_dS < S_BH; (c) the entanglement entropy is finite when S_dS > S_BH. Thus, the de Sitter Hilbert space is effectively nontrivial only when S_dS > S_BH. The AdS black hole we introduce can be regarded as an “observer” for de Sitter space. In this sense, our result is a non-perturbative generalization of the recent perturbative argument that the algebra of observables on the de Sitter static patch becomes nontrivial in the presence of an observer.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: AC02-05CH11231; SC0013528; SC0019380
• OSTI ID: 2433816
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2024; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English