Emergent classical universes from initial quantum states in a tomographical description

Abstract

Quantum and classical physical states are represented in a unified way when they aredescribed 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 a previous work on the de Sitter universe this was done by comparing the classical limit of the quantum tomograms with those 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 find the necessary conditions to extend the previous results by taking the tomograms of the WKB solutions of the Wheeler–DeWitt equation with an 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.