Late-time evolution of the flat Friedmann universe over non-Archimedean space

Abstract

The paper discusses the classical and quantum aspects of the dynamics of the flat Friedmann model of the universe in the late phase of its evolution, predominantly determined by the cosmological constant [Formula: see text]. In the classical part, the Lagrangian of the model is expressed in the Minkowski space and in the Euclidean space in the form of the Lagrangian of the inverted oscillator and the Lagrangian of the standard linear harmonic oscillator, respectively. The classic actions and Feynman propagators were determined as well as the dependence of the scale factor on time in the case of the Minkowski-type metric. Within the quantum part, the asymptotic form of the Wheeler–DeWitt wave function of the model in the considered expanding phase was first determined, and then the vacuum [Formula: see text]-adic states with the specific conditions of their existence. In the generalized adelic approach, a vacuum adelic wave function is constructed, whose form implies minisuperspace discretization.