Volume complexity of dS bubbles

In the framework of the static patch approach to de Sitter holography introduced in [L. Susskind, J. Hologr. Appl. Phys. 1, 1 (2021)], the growth of holographic complexity has a hyperfast behavior, which leads to a divergence in a finite time. This is very different from the anti-de Sitter (AdS) spacetime, where instead the complexity rate asymptotically reaches a constant value. We study holographic volume complexity in a class of asymptotically AdS geometries which include de Sitter bubbles in their interior. With the exception of the static bubble case, the complexity obtained from the volume of the smooth extremal surfaces which are anchored just to the AdS boundary has a similar behavior to the AdS case, because it asymptotically grows linearly with time. The static bubble configuration has a zero complexity rate and corresponds to a discontinuous behavior, which resembles a first order phase transition. If instead we consider extremal surfaces which are anchored at both the AdS boundary and the de Sitter stretched horizon, we find that complexity growth is hyperfast, as in the de Sitter case.

Automated summary

In the framework of de Sitter holography, the growth of holographic complexity shows hyperfast behavior, unlike the case of AdS. Except for static bubble configurations, the complexity obtained from the volume of smooth extremal surfaces anchored on the AdS boundary behaves similarly to the AdS case, while the static bubble configuration exhibits zero complexity rate and resembles a first order phase transition.