Circuit Complexity From Cosmological Islands

TL;DR

This work probes cosmological circuit complexity in FLRW spacetimes with and without Quantum Extremal Islands (AdS/dS cases) by recasting cosmological perturbations into a two-mode squeezed-state framework. Using the Mukhanov–Sasaki formalism and Nielsen’s circuit complexity, it expresses complexity, OTOCs, and entanglement entropy in terms of squeezing parameters $r_k$ and $\phi_k$, and analyzes two dynamical scale-factor models (AdS with radiation and dS with radiation). The study demonstrates non-universality: complexity and chaos indicators depend sensitively on the cosmological parameter space and island presence, with AdS/Island cases tending to Page-curve–like complexity behavior while dS/no-Island cases do not. The results highlight a model-dependent linkage between quantum chaos diagnostics and gravitational island physics, offering a tractable, gravity-agnostic route to explore island-related information questions via circuit complexity and squeezing dynamics.

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.

Figures (29)

• Figure 2.1: Schematic diagram showing the entropy of the outgoing radiation of the evaporating black hole as a function of physical evolutionary time scale. This schematic diagram was taken from Almheiri:2020cfm.
• Figure 3.1: Representative Penrose diagram of recollapsing FRW cosmology with radiation and negative cosmological constant showing presence of Islands. This diagram has been taken from Hartman:2020khs
• Figure 4.1: Penrose diagram showing regions of FRW cosmology with radiation and positive cosmological constant. It shows that the Bekenstein violating region does not overlap with the quantum normal region. Hence it does not contain any islands. This diagram has been taken from Hartman:2020khs
• Figure 7.1: Squeezed state parameter $r_k$ plotted against scale factor.
• Figure 7.2: Squeezing angle $\phi_k$ plotted against scale factor