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The out-of-time-ordered correlation (OTOC) function is an important new probein quantum field theory which is treated as a significant measure of randomquantum correlations. In this paper, with the slogan "Cosmology meets CondensedMatter Physics" we demonstrate a formalism using which for the first time wecompute the Cosmological OTOC during the stochastic particle production duringinflation and reheating following canonical quantization technique. In thiscomputation, two dynamical time scales are involved, out of them at one timescale the cosmological perturbation variable and for the other the canonicallyconjugate momentum is defined, which is the strict requirement to define timescale separated quantum operators for OTOC and perfectly consistent with thegeneral definition of OTOC. Most importantly, using the present formalism notonly one can study the quantum correlation during stochastic inflation andreheating, but also study quantum correlation for any random events inCosmology. Next, using the late time exponential decay of cosmological OTOCwith respect to the dynamical time scale of our universe which is associatedwith the canonically conjugate momentum operator in this formalism we study thephenomena of quantum chaos by computing the expression for {\it Lyapunovspectrum}. Further, using the well known Maldacena Shenker Stanford (MSS)bound, on Lyapunov exponent, $\lambda\leq 2\pi/\beta$, we propose a lower boundon the equilibrium temperature, $T=1/\beta$, at the very late time scale of theuniverse. On the other hand, with respect to the other time scale with whichthe perturbation variable is associated, we find decreasing but notexponentially decaying behaviour, which quantifies the random correlation atout-of-equilibrium. Finally, we have studied the classical limit of the OTOC tocheck the consistency with the large time limiting behaviour.

symmetry

The Cosmological OTOC: Formulating new cosmological micro-canonical  correlation functions for random chaotic fluctuations in Out-of-Equilibrium  Quantum Statistical Field Theory