Particle production in the background with VEV depending on time

It is known that time-dependent vacuum expectation value of the background field may lead to abundant particle production in the early Universe. In supersymmetric theories bosons and fermions are produced in a correlated manner that depends on the details of the supersymmetric scenario. Paper presents the general method of calculating the number density of produced particles based on the WKB approximation and the generalized Bogoliubov transformation law. The impact of the backreaction and rescattering is emphasized, also in models with more than one coupling constant.