  The out-of-time-ordered correlation (OTOC) function is an important new probe
in quantum field theory which is treated as a significant measure of random
quantum correlations. In this paper, with the slogan "Cosmology meets Condensed
Matter Physics" we demonstrate a formalism using which for the first time we
compute the Cosmological OTOC during the stochastic particle production during
inflation and reheating following canonical quantization technique. In this
computation, two dynamical time scales are involved, out of them at one time
scale the cosmological perturbation variable and for the other the canonically
conjugate momentum is defined, which is the strict requirement to define time
scale separated quantum operators for OTOC and perfectly consistent with the
general definition of OTOC. Most importantly, using the present formalism not
only one can study the quantum correlation during stochastic inflation and
reheating, but also study quantum correlation for any random events in
Cosmology. Next, using the late time exponential decay of cosmological OTOC
with respect to the dynamical time scale of our universe which is associated
with the canonically conjugate momentum operator in this formalism we study the
phenomena of quantum chaos by computing the expression for {\it Lyapunov
spectrum}. Further, using the well known Maldacena Shenker Stanford (MSS)
bound, on Lyapunov exponent, $\lambda\leq 2\pi/\beta$, we propose a lower bound
on the equilibrium temperature, $T=1/\beta$, at the very late time scale of the
universe. On the other hand, with respect to the other time scale with which
the perturbation variable is associated, we find decreasing but not
exponentially decaying behaviour, which quantifies the random correlation at
out-of-equilibrium. Finally, we have studied the classical limit of the OTOC to
check the consistency with the large time limiting behaviour.
