Abstract
In this work, our prime focus is to study the one to one correspondence between the conduction phenomena in electrical wires with impurity and the scattering events responsible for particle production during stochastic inflation and reheating implemented under a closed quantum mechanical system in early universe cosmology. In this connection, we also present a derivation of quantum corrected version of the Fokker–Planck equation without dissipation and its fourth order corrected analytical solution for the probability distribution profile responsible for studying the dynamical features of the particle creation events in the stochastic inflation and reheating stage of the universe. It is explicitly shown from our computation that quantum corrected Fokker–Planck equation describe the particle creation phenomena better for Dirac delta type of scatterer. In this connection, we additionally discuss Itô, Stratonovich prescription and the explicit role of finite temperature effective potential for solving the probability distribution profile. Furthermore, we extend our discussion of particle production phenomena to describe the quantum description of randomness involved in the dynamics. We also present computation to derive the expression for the measure of the stochastic non-linearity (randomness or chaos) arising in the stochastic inflation and reheating epoch of the universe, often described by Lyapunov Exponent. Apart from that, we quantify the quantum chaos arising in a closed system by a more strong measure, commonly known as Spectral Form Factor using the principles of random matrix theory (RMT). Additionally, we discuss the role of out of time order correlation function (OTOC) to describe quantum chaos in the present non-equilibrium field theoretic setup and its consequences in early universe cosmology (stochastic inflation and reheating). Finally, for completeness, we also provide a bound on the measure of quantum chaos (i.e. on Lyapunov Exponent and Spectral Form Factor) arising due to the presence of stochastic non-linear dynamical interactions into the closed quantum system of the early universe in a completely model-independent way.
Highlights
A non-adiabatic change in the time dependent effective mass profiles of the fields as the background evolution of the fields passes through special points in field space produces these burst of particle creation in de Sitter space time
In this paper, we have provided the analogy between particle creation in primordial cosmology and scattering problem inside a conduction wire in presence of impurities
Specific time dependence of mass profile restricts the structure of the scattering effective potential
Summary
Quantum fields in an inflationary background [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] or during reheating [26,27,28,29,30,31,32] gives rise to the burst of particle production, which has been extensively studied in Refs. [33,34,35]. While calculating the Fokker–Planck dynamics we observe that the skewness gives us a clue about the rate at which the particle production occurs meaning that longer the trailing part of the profile more is the number density of particles in the scattering event for a given time in the frame of the observer, whereas, kurtosis tells us the width of the probability distribution function which is essentially the amplitude with which the particle production phenomena occurs, which more suggestively tells us about the standard deviation of the density function from Gaussianity This may be a signature of non-Gaussianity that arises in various models in early universe cosmology.
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