Quantum corrections to the Classical Statistical Approximation for the expanding quantum field

Abstract

We found the deviation of the equation of state from ultrarelativistic one due to quantum corrections for a nonequilibrium longitudinally expanding scalar field. Relaxation of highly excited quantum field is usually described in terms of Classical Statistical Approximation (CSA). However, the expansion of the system reduces the applicability of such a semiclassical approach as the CSA making quantum corrections important. We calculate the evolution of the trace of the energy-momentum tensor within the Keldysh-Schwinger framework for static and longitudinal expanding geometries. We provide analytical and numerical arguments for the appearance of the nontrivial intermediate regime where quantum corrections are significant.