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Canonical wave packets in quantum cosmology

Siamak Sadat Gousheh, Hamid Reza Sepangi, Pouria Pedram, M. Mirzaei

Published Jan 1, 2008• 13 citations
OpenAlex

Abstract

We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a “canonical initial slope ” for a given initial wave function, which optimizes some desirable properties of the resulting wave packet, most importantly good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is generalization of our earlier work. PACS numbers: 04.20.Ex, 04.60.Kz, 04.25.-g 1

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We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a “canonical initial slope ” for a given initial wave function, which optimizes some desirable properties of the resulting wave packet, most importantly good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is generalization of our earlier work. PACS numbers: 04.20.Ex, 04.60.Kz, 04.25.-g 1
We discuss the construction of wave packets resulting from solutions of a class of Wheeler–DeWitt equations in Robertson–Walker-type cosmologies, for arbitrary curvature. We show that there always exists a 'canonical initial slope' for a given initial wavefunction, which optimizes some desirable properties of the resulting wave packet, most importantly a good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is a generalization of our earlier work.
We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of ‘canonical ’ wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in the Stephani Universe. We suggest appropriate initial conditions which result in wave packets containing some desirable properties, most importantly good classical and quantum correspondence. We also study the situation from de-Broglie Bohm interpretation of quantum mechanics to recover the notion of time and compare the classical and Bohmian results. We exhibit that the usage of the canonical prescription and appropriate choices of expansion coefficients result in the suppression of the quantum potential and coincidence between classical and Bohmian results. We show that, in some cases, contrary to Friedmann-Robertson-Walker case, the bound state solutions also exist for all positive values of the cosmological constant. Pacs: 98.80.Qc, 04.40.Nr, 04.60.Ds; 1
We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of 'canonical' wavepackets resulting from the solutions of a class of Wheeler–DeWitt equations in the Stephani Universe. We suggest appropriate initial conditions which result in wavepackets containing some desirable properties, most importantly good classical and quantum correspondence. We also study the situation from the de Broglie–Bohm interpretation of quantum mechanics viewpoint to recover the notion of time and compare the classical and Bohmian results. We show the usage of the canonical prescription and appropriate choices of expansion coefficients to result in the suppression of the quantum potential and coincidence of classical and Bohmian results. We show that, in some cases, contrary to the Friedmann–Robertson–Walker case, the bound state solutions also exist for all positive values of the cosmological constant.
We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmology with a free, massless, minimally coupled scalar field, thus providing a complete decoherent histories formulation for this quantum cosmological model. The decoherence functional is applied to study predictions concerning the model's Dirac (relational) observables; the behavior of semiclassical states and superpositions of such states; and to study the singular behavior of quantum Wheeler-DeWitt universes. Within this framework, rigorous formulas are given for calculating the corresponding probabilities from the wave function when those probabilities may be consistently defined, thus replacing earlier heuristics for interpreting the wave function of the universe with explicit constructions. It is shown according to a rigorously formulated standard, and in a quantum-mechanically consistent way, that in this quantization these models are generically singular. Independent of the choice of state we show that the probability for these Wheeler-DeWitt quantum universes to ever encounter a singularity is unity. In addition, the relation between histories formulations of quantum theory and relational Dirac observables is clarified.
For a FRW-spacetime coupled to an arbitrary real scalar field, we endow the solution space of the associated Wheeler-DeWitt equation with a Hilbert-space structure, construct the observables, and introduce the physical wave functions of the universe that admit a genuine probabilistic interpretation. We also discuss a proposal for the formulation of the dynamics. The approach to quantum cosmology outlined in this article is based on the results obtained within the theory of pseudo-Hermitian operators. 1