  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.
