Circuit Complexity From Cosmological Islands

TL;DR

This paper explores how quantum extremal islands influence cosmological circuit complexity, entanglement entropy, and OTOCs in FLRW spacetime, revealing their non-universal behavior across different cosmological models.

Contribution

It introduces a model-independent analysis of cosmological circuit complexity in the presence or absence of quantum extremal islands in FLRW spacetime.

Findings

Circuit complexity varies with cosmological parameters.

Entanglement entropy and OTOCs show non-universal features.

Different parameter spaces lead to distinct complexity behaviors.

Abstract

Recently in various theoretical works, path-breaking progress has been made in recovering the well-known Page Curve of an evaporating black hole with Quantum Extremal Islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of Quantum Extremal Islands in the negative (or positive) Cosmological Constant with radiation in the background of Friedmann-Lema$\hat{i}$tre-Robertson-Walker (FLRW) space-time i.e the presence and absence of islands in anti-de Sitter and the de Sitter spacetime having SO(2, 3) and SO(1, 4) isometries respectively. Without using any explicit details of any gravity model, we study the behaviour of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above-mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, Out-of-Time Ordered Correlators, and entanglement entropy of the modes of the squeezed state, in different parameter spaces, we conclude the non-universality of these measures. Their remarkably different features in the different parameter spaces suggest their dependence on the parameters of the model under consideration.