Classical universe emerging from quantum cosmology without horizon and flatness problems

Abstract

We apply the complex de Broglie-Bohm formulation of quantum mechanics in Chou and Wyatt (Phys Rev A 76: 012115, 2007), Gozzi (Phys Lett B 165: 351, 1985), Bhalla et al. (Am J Phys 65: 1187) to a spatially closed homogeneous and isotropic early universe whose matter contents are radiation and dust perfect fluids. We then show that an expanding classical universe can emerge from an oscillating (with complex scale factor) quantum universe without singularity. Furthermore, the universe obtained in this process has no horizon or flatness problems.

Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation

“…The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in [1]. In this paper we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics, applied to quantum cosmology.…”

“…Recently, in [1] the QHJ formulation of quantum cosmology is developed. The authors obtained the state dependent quantum cosmological solutions with complex trajectories in the complex minisuperspace.…”

“…In this section we will review briefly the minisuperspace quantum cosmological models in the framework of QHJ developed by Fathi, Jalalzadeh and Moniz in [1]. Let us start with the line element of spacetime which is given by…”

“…Let us now review the minisuperspace quantum cosmology in the context of QHJ formalism developed in [1]. The complex-valued QHJ equation is readily obtained by substituting the polar form of the complex-valued wave function [3] Ψ(q µ ) = e iS(q µ ) , q µ and S(q µ ) ∈ C,…”

The quantum state of the universe from deformation quantization and classical-quantum correlation

“…Nevertheless, there are some alternative solutions to the above quantum cosmological difficulties, which together with decoherence may solve the measurement problem maintaining the universality of quantum theory and emergence of classical universe. In this line we should cite the de Broglie-Bohm interpretation of quantum cosmology [11], quantum Hamilton-Jacobi cosmology [12] and deformation quantization of cosmology [13].…”