Classical versus quantum features of the Berthelot cosmological model

Abstract

In this paper, we compare and contrast the classical versus quantum dynamics of a cosmological model based on the literature (Modified) Berthelot equation of state for the description of the dark sector of the universe. At the classical background level we identify a Minkowski-like and a de Sitter-like equilibrium epochs, with the latter occurring only beyond a certain threshold for a parameter in the equation of state; at the classical perturbed level we find that this same parameter realizes a duality in the adiabatic speed of sound between the two equilibrium epochs. The quantum evolution of this model is studied in the context of quantum geometrodynamics by solving analytically the Wheeler–DeWitt equation in the Born–Oppenheimer approximation for the scalar field potentials about the two equilibrium epochs. We identify the phenomenon of quantum decoherence to arise at the same threshold which constitutes the bifurcation between the two equilibrium epochs at the classical level. We comment on the quantum modified power spectrum focusing on some consequences dealing with the formation of astrophysical structures within the Press–Schechter framework. Our paper is intended to scrutinize which classical features of a certain cosmological model are preserved at its quantum level, and under which assumptions.