Classical and quantum behavior of the generic cosmological solution

Giovanni Imponente, Giovanni Montani

Research output: Contribution to conferencePaper

3 Citations (Scopus)

Abstract

In the present paper we generalize the original work of C.W. Misner [1] about the quantum dynamics of the Bianchi type IX geometry near the cosmological singularity.We extend the analysis to the generic inhomogeneous universe by solving the super-momentum constraint and outlining the dynamical decoupling of spatial points. Firstly, we discuss the classical evolution of the model in terms of the Hamilton-Jacobi approach as applied to the super-momentum and super-Hamiltonian constraints; then we quantize it in the approximation of a square potential well after an ADM reduction of the dynamics with respect to the super-momentum constraint only. Such a reduction relies on a suitable form for the generic three-metric tensor which allows the use of its three functions as the new spatial coordinates. We get a functional representation of the quantum dynamics which is equivalent to theMisner-like one when extended point by point, since the Hilbert space factorizes into ∞3 independent components due to the parametric role that the three-coordinates assume in the asymptotic potential term. Finally, we discuss the conditions for having a semiclassical behavior of the dynamics and we recognize that this already corresponds to having mean occupation numbers of order O(102). © 2006 American Institute of Physics.
Original languageEnglish
DOIs
Publication statusPublished - 2006
Externally publishedYes
EventAlbert Einstein Century International Conference - , France
Duration: 1 Jan 2006 → …

Conference

ConferenceAlbert Einstein Century International Conference
CountryFrance
Period1/1/06 → …

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Imponente, G., & Montani, G. (2006). Classical and quantum behavior of the generic cosmological solution. Paper presented at Albert Einstein Century International Conference, France. https://doi.org/10.1063/1.2399600