Emergence of quantum chaos in non-equilibrium cosmology

The early universe is likely filled with a large number of interacting fields with unknown interactions. How can we quantitatively understand particle production (for example, during inflation and reheating after inflation) when such fields undergo a sufficient number of non-adiabatic, non-perturbative interactions? A recent proposal of a precise mapping between stochastic particle production events during inflation and re-heating in cosmology to conduction phenomena in disordered quasi one-dimensional wires provide a powerful statistical framework to resolve such seemingly intractable calculations. In my talk, I will describe our work where we use this precise correspondence to present a novel derivation for quantum corrections to the Fokker-Planck equation without dissipation responsible for studying the dynamical features of such stochastic particle creation events during the inflationary and re-heating epoch of the universe. Stochastic particle creation events can involve a large number of non-adiabatic events (scatterings). Such non-linearities give rise to signatures of quantum chaos. I will discuss our computation on the role of out-of-time ordered correlators to describe quantum chaos in the present non-equilibrium field theoretic setup and its consequences in stochastic inflation and reheating epoch of the universe using Spectral Form Factors from the principles of Gaussian Random Matrix Theory. Furthermore, my talk will focus on our proposed bound on the rate of growth of quantum chaos during stochastic particle production events in the early universe for non-adiabatic couplings with Gaussian matrix-models, namely polynomial matrix-models of Wigner-Dyson type.