Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Cosmological OTOC: A New Proposal for Quantifying Auto-correlated Random Non-chaotic Primordial Fluctuations

Version 1 : Received: 26 February 2021 / Approved: 26 February 2021 / Online: 26 February 2021 (12:05:23 CET)
Version 2 : Received: 30 March 2021 / Approved: 30 March 2021 / Online: 30 March 2021 (10:42:46 CEST)

How to cite: Choudhury, S. The Cosmological OTOC: A New Proposal for Quantifying Auto-correlated Random Non-chaotic Primordial Fluctuations. Preprints 2021, 2021020616 (doi: 10.20944/preprints202102.0616.v1). Choudhury, S. The Cosmological OTOC: A New Proposal for Quantifying Auto-correlated Random Non-chaotic Primordial Fluctuations. Preprints 2021, 2021020616 (doi: 10.20944/preprints202102.0616.v1).

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 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 the cases we found significantly distinguishable non-chaotic, but random behaviour in the OTO auto-correlations, which was not pointed before in this type of studies. 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 exactly matches with the large time limiting behaviour of the auto-correlations in the super-horizon regime of the cosmological scalar mode fluctuation.

Subject Areas

Quantum Correlation; QFT in De Sitter space; Out-of-equilibrium aspects of Cosmology; Out-of-time ordered correlators

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