The cosmological switchback effect. Part II

Recent developments in static patch holography proposed that quantum gravity in de Sitter space admits a dual description in terms of a quantum mechanical theory living on a timelike surface near the cosmological horizon. In parallel, geometric observables associated with the Einstein-Rosen bridge of a black hole background were suggested to compute the computational complexity of the state dual to a gravitational theory. In this work, we pursue the study of the complexity=volume and complexity=action conjectures in a Schwarzschild-de Sitter geometry perturbed by the insertion of a shockwave at finite boundary times. This analysis extends previous studies that focused either on the complexity=volume 2.0 conjecture, or on the case of a shockwave inserted along the cosmological horizon. We show that the switchback effect, describing the delay in the evolution of complexity in reaction to a perturbation, is a universal feature of the complexity proposals in asymptotically de Sitter space. The geometric origin of this phenomenon is related to the causal connection between the static patches of de Sitter space when a positive pulse of null energy is inserted in the geometry.