Subregion complexity in holographic thermalization with dS boundary

Abstract

We study the time evolution of holographic subregion complexity (HSC) in Vaidya spacetime with dS boundary. The subregion on the boundary is chosen to be a sphere within the cosmological horizon. It is found that the behaviour of HSC is similar to that in cases with flat boundary. The whole evolution can be divided into four stages: First, it grows almost linearly, then the growth slows down; After reaching a maximum it drops down quickly and gets to saturation finally. The linear growth rate in the first stage is found to depend almost only on the the mass parameter. As the subregion size approaches the cosmological horizon, this stage is expected to last forever with the subsequent three stages washed out. The saturation time ${\tilde{t}}_{sat}$ depends almost only on the subregion size $\tilde{R}$ as ${\tilde{t}}_{sat}={\tanh }^{-1}(\tilde{R})$ which is linear in $\tilde{R}$ when $\tilde{R}$ is small but logarithmically divergent as $\tilde{R}$ approaches the cosmological horizon.

v1: 21 pages, 6 figures; v2: refs added, minor modifications; v3: typos corrected, to match the published version

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• Holographic Subregion Complexity in General Vaidya Geometry
• Non-Conformality, Subregion Complexity and Meson Binding
• A note on holographic subregion complexity and QCD phase transition
• Complexity and uncomplexity during energy injection
• Probes of holographic thermalization in a simple model with momentum relaxation
• Membrane nucleation rates from holography
• Resource and stability near a critical point from the quantum information perspective
• Switchback effect of holographic complexity in multiple-horizon black holes