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Inhomogeneous quantum cosmology: An infinite-parameter model
Phys. Rev. D 41, 3671 – Published 15 June, 1990
DOI: https://doi.org/10.1103/PhysRevD.41.3671
Abstract
A generalized version of Gowdy spacetime is studied and a proposal for an approximation scheme made that allows for some study of its quantum behavior in the Hartle-Hawking prescription. The system is reduced in freedom to an infinite-parameter midisuperspace model and the reduced system is analyzed. The measure choice turns out to be difficult. The system is solved up to one loop and the behavior of the partition function with respect to scaling of the metric in the direction transverse to the propagation of gravitational waves is examined. It is found that the scaling of the WKB prefactor depends only on topological factors and that this suggests that the model evolves from a pure state to a mixed one. The relation to the arrow of time is discussed. A crude reduction to dynamical degrees of freedom is made, and the possibility of creating a manifestly convergent Euclidean formalism is discussed. Some open questions as to the nature of a sum over topologies are examined via both the Page and Hawking proposals. Convergence of the partition function is examined. The possibility of a transition in behavior at a critical scale is discussed.
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