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.
Highlights
Background field in Friedmann–Lemaître–Robertson– Walker (FLRW) Perturbation inFLRW (121)to express the whole dynamics in terms of a gauge invariant description through a variable: Perturbation variable : ζ(x, τ) = −H(τ) dφ(τ) dτ δφ(x, t)Perturbation in FLRW
Our objective is to explore the behaviour of the quantum correlation functions in the outof-equilibrium regime of the quantum field theory of primordial cosmology appearing in the early time scale of the evolution of our universe
First of all, in this paper we have provided a computation using which it is possible to derive the expressions for the two specific types of of-time ordered correlation (OTOC) made up of cosmological scalar perturbation field variables and its associated canonically conjugate momentum variable auto-correlations to study the feature of randomness without having chaotic behaviour in a primordial cosmology setup
Summary
The underlying physical concept of out-of-time ordered correlation (OTOC) functions [1–9] within the framework of quantum field theory is considered to be a very strong theoretical tool to describe random phenomena in the quantum regime, the phenomena of quantum chaos. One of the well-known examples of these classes of models is the quantum harmonic oscillator (QHO) which can be solely represented by the contributions from the microcanonical part after summing over all possible eigenstates of the Hamiltonian of the QHO In this connection here, it is important to note that, at the perturbation level, cosmology with a free massive scalar field theory in an FLRW space-time can be represented as a quantum parametric oscillator with a time-dependent frequency in the Fourier space, but instead of having a harmonic oscillator type of representation within the framework of quantum mechanical framework of cosmology, we do not have any eigenstates Instead of having a eigenstate in the context of cosmology one can define wave function of the universe and instead of having a discrete eigen energy spectrum in the context of cosmology we can find a continuous time-dependent momentum integrated spectrum over all Fourier modes
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