Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-09-25
Phys.Rev.D67:024019,2003
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
26 pages including 10 figures, some reorganization in the presentation of results, expanded discussion of results in the conte
Scientific paper
10.1103/PhysRevD.67.024019
We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge formulation of gravity in three dimensions. We consider the behavior of conditional probabilities and expectation values for geometrical quantities in this initial state for a simple minisuperspace model consisting of a two-parameter set of anisotropic geometries on a 2-sphere boundary. We find dependence on the cutoff used in the construction of Ponzano-Regge amplitudes for expectation values of edge lengths. However, these expectation values are cutoff independent when computed in certain, but not all, conditional probability distributions. Conditions that yield cutoff independent expectation values are those that constrain the boundary geometry to a finite range of edge lengths. We argue that such conditions have a correspondence to fixing a range of local time, as classically associated with the area of a surface for spatially closed cosmologies. Thus these results may hint at how classical spacetime emerges from quantum amplitudes.
Petryk Roman
Schleich Kristin
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