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Complexity in de Sitter space

Reynolds, Alan P.; Ross, Simon F.

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Alan P. Reynolds


We consider the holographic complexity conjectures for de-Sitter invariant states in a quantum field theory on de Sitter space, dual to asymptotically anti-de Sitter geometries with de Sitter boundaries. The bulk holographic duals include solutions with or without a horizon. If we compute the complexity from the spatial volume, we find results consistent with general expectations, but the conjectured bound on the growth rate is not saturated. If we compute complexity from the action of the Wheeler–de Witt patch, we find qualitative differences from the volume calculation, with states of smaller energy having larger complexity than those of larger energy, even though the latter have bulk horizons.


Reynolds, A. P., & Ross, S. F. (2017). Complexity in de Sitter space. Classical and Quantum Gravity, 34(17), Article 175013.

Journal Article Type Article
Acceptance Date Jul 20, 2017
Online Publication Date Aug 10, 2017
Publication Date Aug 10, 2017
Deposit Date Aug 11, 2017
Publicly Available Date Aug 10, 2018
Journal Classical and Quantum Gravity
Print ISSN 0264-9381
Electronic ISSN 1361-6382
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 34
Issue 17
Article Number 175013
Related Public URLs


Accepted Journal Article (662 Kb)

Copyright Statement
This is an author-created, un-copyedited version of an article published in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at

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