Seminarium Teorii Względności i Grawitacji

Determining the dynamics of quantum systems beyond simplest 'textbook' ones on the genuine quantum level is usually very computationally expansive to the level of impractical. In cases, when the point of focus is the evolution of the semiclassical states, an alternative approach based on the so called Hamburger decomposition can be taken. There, one encodes the information about the state in the countable set of (expectation values of the) observables -- the moments, which essentially are the polynomial decomposition coefficients of the Wigner quasi-probability distribution. The set of the equations of motion for these moments is equivalent to a genuine quantum evolution, however a convenient cutoff (on the order of the moments) can be introduced, leaving just a couple of most relevant degrees of freedom. The accuracy of the resulting effective dynamics depends on the order of cutoff and the properties of particular system. In this presentation I will discuss the result of application of this (long known) formalism to a simple quantum model of inflationary cosmology, studying in particular the issue of accuracy of the description and effect of high order quantum corrections on Universe dynamics. I will present the case, where the high order effects significantly change the conclusions drawn from models including just the 2nd order moments (variances), in particular significant corrections may actually compensate the effects of variances making the evolution more classical.