Complexity in de Sitter Space

Abstract

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.

29 pages, v2: references added

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Cited by in corpus (58)

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• Complexity and entanglement for thermofield double states
• Circuit complexity for free fermions
• Circuit complexity in interacting QFTs and RG flows
• Holographic Complexity in Vaidya Spacetimes II
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Circuit Complexity for Coherent States
• Subsystem Complexity and Holography
• Time Evolution of Complexity: A Critique of Three Methods
• Holographic Complexity in Vaidya Spacetimes I
• Holographic Complexity of Einstein-Maxwell-Dilaton Gravity
• Holographic Complexity Equals Which Action?
• The First Law of Complexity
• Pure de Sitter space and the island moving back in time
• Cosmological Complexity
• Entangling power and quantum circuit complexity
• Black holes in dS${}_3$
• Holographic Complexity and de Sitter Space
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Action growth rate for a higher curvature gravitational theory
• Cosmological Krylov Complexity
• Circuit Complexity for Fermionic Thermofield Double states
• De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity
• Complexity of AdS_5 black holes with a rotating string
• On Complexity Growth in Minimal Massive 3D Gravity
• Quantum Kerr-de Sitter black holes in three dimensions
• Complexity and phase transitions in a holographic QCD model
• Complexity growth of rotating black holes with a probe string
• Modified "complexity equals action" conjecture
• Investigating two counting methods of the holographic complexity
• Holographic complexity in charged Vaidya black hole
• Holographic complexity growth in a FLRW universe
• Null boundary terms for Lanczos-Lovelock gravity
• Holographic complexity of charged Taub-NUT-AdS black holes
• Revisit on holographic complexity in two-dimensional gravity
• Holographic complexity of the electromagnetic black hole
• Holographic complexity of Born-Infeld black holes
• Complexity of non-trivial sound speed in inflation
• Subregion complexity in holographic thermalization with dS boundary
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• Subregion complexity and confinement-deconfinement transition in a holographic QCD model
• Complexity growth of massive black hole with a probe string
• Emergent $\alpha$-like fermionic vacuum structure and entanglement in the hyperbolic de Sitter spacetime
• Holographic Complexity in a Charged Supersymmetric Black Holes
• Holographic Complexity and Phase Transition for AdS Black Holes
• Cosmological complexity of the modified dispersion relation
• Complexity growth for topological black holes by holographic method
• Gauss-Bonnet AdS planar and spherical black hole thermodynamics and holography
• Generalized holographic complexity of rotating black holes
• Weighting gates in circuit complexity and holography
• Complexity growth of BTZ black hole in massive gravity with a null string
• Causality Constraint on Circuit Complexity from $COSMOEFT$
• Field theory aspects of $\eta$-deformed superstring background
• Quantum fluctuation on the worldsheet of probe string in BTZ black hole
• Finite complexity of the de Sitter vacuum
• Switchback effect of holographic complexity in multiple-horizon black holes
• Holographic timelike entanglement and $c$ theorem for supersymmetric QFTs in ($0+1$)d
• Massive holographic QFTs in de Sitter