The Squeezed OTOC and Cosmology

TL;DR

This paper explores how highly squeezed quantum states in cosmology exhibit exponential growth in the out-of-time-order correlator (OTOC), indicating quantum chaos, especially in expanding de Sitter backgrounds, with implications for understanding cosmological perturbations.

Contribution

It introduces a quantum Lyapunov spectrum method for squeezed states and applies OTOC analysis to various cosmological backgrounds, revealing universal growth behavior.

Findings

OTOC for highly squeezed states is exponentially large.

Expanding de Sitter backgrounds support exponential OTOC growth.

OTOC growth proportional to scale factor for super-Hubble perturbations.

Abstract

Exponential growth in the out-of-time-order correlator (OTOC) is an important potential signature of quantum chaos. The OTOC is quite simple to calculate for squeezed states, whose applications are frequently found in quantum optics and cosmology. We find that the OTOC for a generic highly squeezed quantum state is exponentially large, suggesting that highly squeezed states are "primed" for quantum chaos. A quantum generalization of the classical symplectic phase space matrix can be used to extract the quantum Lyapunov spectrum, and we find this better captures the exponential growth of squeezed states for all squeezing angles compared to any single OTOC. By describing cosmological perturbations in the squeezed state language, we are able to apply our calculations of the OTOC to arbitrary expanding and contracting backgrounds with fixed equation of state. We find that only expanding de Sitter backgrounds support an exponentially growing OTOC at late times, with a putative Lyapunov exponent consistent with other calculations. While the late-time behavior of the OTOC for other cosmological backgrounds appears to change depending on the equation of state, we find that the quantum Lyapunov spectrum shows some universal behavior: the OTOC grows proportional to the scale factor for perturbation wavelengths larger than the cosmological Hubble horizon.