Shock waves and delay of hyperfast growth in de Sitter complexity

We study the holographic complexity in de Sitter spacetime, especially how the hyperfast growth of holographic complexity in de Sitter spacetime is affected under a small and early perturbation. The perturbed geometry is de Sitter spacetime with shock waves. We find that the critical time, at which de Sitter holographic complexity diverges, becomes always greater in the presence of the shock waves, which satisfies the averaged null energy conditions. This means that the hyperfast property of de Sitter complexity is delayed by small perturbations.