Quantum Out-of-Equilibrium Cosmology
  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
fourth order corrected version of the Fokker Planck equation and its analytical
solution 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 It$\hat{o}$,
Stratonovich prescription and the explicit role of finite temperature effective
potential for solving the probability distribution profile. Furthermore, we
extend our discussion to describe the quantum description of randomness
involved in the dynamics. We also present a computation to derive the
expression for the measure of the stochastic non-linearity 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 (OTOC) function to describe quantum
chaos in the present non-equilibrium field theoretic setup. Finally, for
completeness, we also provide a bound on the measure of quantum chaos 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.
