THE CWKB PARTICLE PRODUCTION AND CLASSICAL CONDENSATE IN DE SITTER SPACE–TIME

Abstract

The complex time WKB approximation is an effective tool in studying particle production in curved space–time. We use it in this work to understand the formation of classical condensate in expanding de Sitter space–time. The CWKB leads to the emergence of thermal spectrum that depends crucially on horizons (as in de Sitter space–time) or observer dependent horizons (as in Rindler space–time). A connection is sought between the horizon and the formation of classical condensate. We concentrate on de Sitter space–time and study the cosmological perturbation of k = 0 mode with various values of m/H0. We find that, for a minimally coupled free scalar field for [Formula: see text], the one-mode occupation number grows more than unity soon after the physical wavelength of the mode crosses the Hubble radius and soon after that, diverges as [Formula: see text], where [Formula: see text]. The results substantiate the previous works in this direction. We also find the correct oscillation and behavior of N(z) at small z from a single expression using CWKB approximation for various values of m/H0. We also discuss decoherence in relation to the formation of classical condensate. We further find that the squeezed state formalism and CWKB method give identical results.