Emergent classical universes from initial quantum states in a tomographical description

TL;DR

This paper uses symplectic tomography to analyze how classical universes can emerge from quantum states, extending previous de Sitter universe results to more general models and proposing a phenomenological approach to initial states.

Contribution

It extends the symplectic tomography framework to all de Sitter models and general potentials, linking quantum and classical descriptions through the Wheeler-DeWitt equation.

Findings

Necessary conditions for classical universe emergence identified

Tomograms derived directly from Wheeler-DeWitt equation

Quantum-to-classical transition linked to cosmological constant decay

Abstract

Quantum and classical physical states are represented in a unified way when they are described by symplectic tomography. Therefore this representation allows us to study directly the necessary conditions for a classical universe to emerge from a quantum state. In the previous study on the de Sitter universe this was done by comparing the classical limit of the quantum tomograms with the tomograms resulting from the classical cosmological equations. In this paper we first review these results and extend them to all the de Sitter models. We show further that these tomograms can be obtained directly from transposing the Wheeler-De Witt equation to the tomographic variables. Subsequently, because the classic limits of the quantum tomograms are identified with their asymptotic expressions, we found the necessary conditions to extend the previous results by taking the tomograms of the WKB solutions of the Wheeler-DeWitt equation with a any potential. Furthermore in the previous works we found that the de Sitter models undergo the quantum-to-classical transition when the cosmological constant decays to its present value, we discuss at the end how far we can extend this result to more general models. In the conclusions, after discussing any improvements and developments of the results of this work, we sketch a phenomenological approach from which to extract information about the initial states of the universe.