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We study the holographic complexity in de Sitter spacetime, especially howthe hyperfast growth of holographic complexity in de Sitter spacetime isaffected under a small and early perturbation. The perturbed geometry is deSitter spacetime with shock waves. We find that the critical time, at which deSitter holographic complexity diverges, becomes always greater in the presenceof the shock waves, which satisfies the averaged null energy conditions. Thismeans that the hyperfast property of de Sitter complexity is delayed by smallperturbations.

Shock waves and delay of hyperfast growth in de Sitter complexity