Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

Abstract

A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.

A phase space description of the FLRW quantum cosmology in Hořava–Lifshitz type gravity

“…It is possible to convert the non-local Hamiltonian constraint to a local one when the spacetime is isotropic and homogeneous [57]. In fact, the local Hamiltonian constraint (2.7) is the same that was used in other previous papers which investigate quantum cosmology in HL gravity [7,40,41,53]. Then, our results should be hold for the non-projectable version in the case when the spacetime is isotropic and homogeneous.…”

“…The Hořava-Lifshitz formulation of gravity is an alternative theory to general relativity which employs higher spatial-derivative terms of the curvature which are added to the Einstein-Hilbert action with the aim of obtaining a renormalizable theory. We consider the action for the projectable model which is given by [7,40,41,53,55]…”

“…The behavior of this system without cosmological constant and which is also adequate for small values of the scale factor was considered by Bernardini et al (see [53]) obtaining analytical solutions of the wave function as well as for the Wigner function of a quasi-Gaussian superposition of those states. In addition, they performed a perturbative analysis when the term with cosmological constant is considered.…”

“…Recently an analysis of the FLRW cosmological model in the HL gravity using the Wigner function was given by Bernardini, Leal and Bertolami [53]. In their article, they take in consideration the time evolution and showed that the association of the quantum variable of time with the radiation energy is a suitable option to move from the quantum to the classical behavior.…”

Anharmonic effects on phase-space quantum profiles: an exact approach

“…Considering that the manipulability of such quantum solutions can be extended to the phasespace, their corresponding Wigner functions have been relevant in describing the interplay between quantum and classical aspects as it has been reported in some preliminary analysis [10,11]. In fact, the Wigner formalism [12] encompasses the phase-space dynamics so as to include quantum effects and to provide a more complete overview of the quantum information encoded by quantum systems.…”