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Title: de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity

Abstract

Here, we investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter space. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). Furthermore, we suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti–de Sitter space.

Authors:
 [1];  [1];  [1];  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1597496
Alternate Identifier(s):
OSTI ID: 1416433
Grant/Contract Number:  
SC0011632
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 96; Journal Issue: 12; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Bao, Ning, Cao, ChunJun, Carroll, Sean M., and Chatwin-Davies, Aidan. de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.96.123536.
Bao, Ning, Cao, ChunJun, Carroll, Sean M., & Chatwin-Davies, Aidan. de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity. United States. doi:10.1103/PhysRevD.96.123536.
Bao, Ning, Cao, ChunJun, Carroll, Sean M., and Chatwin-Davies, Aidan. Fri . "de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity". United States. doi:10.1103/PhysRevD.96.123536. https://www.osti.gov/servlets/purl/1597496.
@article{osti_1597496,
title = {de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity},
author = {Bao, Ning and Cao, ChunJun and Carroll, Sean M. and Chatwin-Davies, Aidan},
abstractNote = {Here, we investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter space. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). Furthermore, we suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti–de Sitter space.},
doi = {10.1103/PhysRevD.96.123536},
journal = {Physical Review D},
number = 12,
volume = 96,
place = {United States},
year = {2017},
month = {12}
}

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