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  • Letter
  • Open Access

Finite complexity of the de Sitter vacuum

Suddhasattwa Brahma1,*, Lucas Hackl2,3,†, Moatsem Hassan1,‡, and Xiancong Luo1,§

  • *Contact author: suddhasattwa.brahma@gmail.com
  • †Contact author: lucas.hackl@unimelb.edu.au
  • ‡Contact author: moatasem1508@yahoo.com
  • §Contact author: x.luo-35@sms.ed.ac.uk
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Phys. Rev. D 111, L101902 – Published 19 May, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L101902

Abstract

The Einstein−Rosen=Einstein−Podolsky−Rosen (ER=EPR) conjecture states that quantum entanglement between boundary degrees of freedom leads to the emergence of bulk spacetime itself. Although this has been tested extensively in string theory for asymptotically anti–de Sitter spacetimes, its implications for an accelerating universe, such as our own, remain less explored. Assuming a cosmic version of ER=EPR for de Sitter space, we explore computational complexity corresponding to long-range entanglement responsible for bulk states on spacelike hypersurfaces. Rather remarkably, we find that the complexity (per unit volume) of the Euclidean vacuum, as an entangled state over two boundary conformal field theory vacua, is finite both in the UV and the IR, which provides additional evidence for “cosmic ER=EPR.” Our result seems to be a universal feature of spacetimes with horizons and, moreover, hints at new features of the thermofield double state for studying thermalization of any quantum system.

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Phys. Rev. D 111, L101902– Published 19 May, 2025
  • Received 4 October 2024
  • Accepted 1 May 2025
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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.

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