The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations

TL;DR

This paper introduces a novel formalism for quantifying auto-correlated out-of-time-ordered correlations (OTOCs) in primordial cosmology, revealing non-chaotic yet random behaviors during the non-equilibrium epoch of the early universe.

Contribution

It develops a new computational method using canonical quantization to analyze two types of auto-correlated OTO functions in primordial cosmology, highlighting their non-chaotic behavior.

Findings

Distinct non-chaotic, random behavior in auto-correlations identified

Classical limit of OTOC functions matches super-horizon behavior

New formalism captures quantum fluctuations in early universe

Abstract

The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by following the canonical quantization technique, we demonstrate a computational method to quantify the two different types of cosmological auto-correlated OTO functions during the epoch when the non-equilibrium features dominates in primordial cosmology. In this formulation, two distinct dynamical time scales are involved to define the quantum mechanical operators arising from the cosmological perturbation scenario. We have provided detailed explanation regarding the necessity of this new formalism to quantify any random events generated from quantum fluctuations in primordial cosmology. We have performed an elaborative computation for the two types of two-point and four-point auto-correlated OTO functions in terms of the cosmological perturbation field variables and its canonically conjugate momenta to quantify random auto-correlations in the non-equilibrium regime. For both of the cases, we found significantly distinguishable non-chaotic, but random, behaviour in the OTO auto-correlations, which was not pointed out before in this type of study. Finally, we have also demonstrated the classical limiting behaviour of the mentioned two types of auto-correlated OTOC functions from the thermally weighted phase-space averaged Poisson brackets, which we found to exactly match the large time limiting behaviour of the auto-correlations in the super-horizon regime of the cosmological scalar mode fluctuation.