C=Anything and the switchback effect in Schwarzschild-de Sitter space

TL;DR

This paper explores the behavior of certain observables in Schwarzschild-de Sitter space within the C=Anything framework, revealing the switchback effect and similarities to anti-de Sitter black holes, with implications for quantum theories.

Contribution

It demonstrates that C=Anything observables in SdS can exhibit the switchback effect and similar growth patterns to those in AdS black holes, expanding understanding of holographic complexity.

Findings

Observables show the same growth rate at early and late times.

Shockwaves cause a decrease in late-time complexity growth.

Some SdS observables mimic AdS black hole behavior.

Abstract

We investigate observables within the framework of the codimension-one C=Anything (CAny) proposal for Schwarzschild-de Sitter (SdS) space under the influence of shockwave sources. Within the proposal, there is a set of time-reversal invariant observables that display the same rate of growth at early and late-times for a background with or without shockwave sources. Once we introduce shockwaves in the weak gravitational coupling regime, there is a decrease in the late-time complexity growth due to cancellations with early-time perturbations, known as the switchback effect. The result shows that some CAny observables in SdS may reproduce the same type of behavior found in anti-de Sitter black holes. We comment on how our results might guide us to new explorations in the putative quantum mechanical theory.