Peaks in the Hartle--Hawking wavefunction from sums over topologies

doi:10.1088/0264-9381/21/2/025

Peaks in the Hartle–Hawking wavefunction from sums over topologies

M Anderson et al 2004 Class. Quantum Grav. 21 729-741 doi: 10.1088/0264-9381/21/2/025

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M Anderson¹, S Carlip², J G Ratcliffe³, S Surya⁴ and S T Tschantz³
¹ Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794, USA
² Department of Physics, University of California, Davis, CA 95616, USA
³ Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
⁴ Raman Research Institute, C V Raman Avenue, Sadashivanagar, Bangalore 560 080, INDIA
E-mail: anderson@math.sunysb.edu, carlip@dirac.ucdavis.edu, John.G.Ratcliffe@Vanderbilt.edu, ssurya@rri.res.in and Steven.T.Tschantz@Vanderbilt.edu

Abstract. Recent developments in 'Einstein Dehn filling' allow the construction of infinitely many Einstein manifolds that have different topologies but are geometrically close to each other. Using these results, we show that for many spatial topologies, the Hartle–Hawking wavefunction for a spacetime with a negative cosmological constant develops sharp peaks at certain calculable geometries. The peaks we find are all centred on spatial metrics of constant negative curvature, suggesting a new mechanism for obtaining local homogeneity in quantum cosmology.

PACS numbers: 04.60.Gw, 98.80.Qc, 98.80.Bp

Print publication: Issue 2 (21 January 2004)
Received 10 October 2003
Published 23 December 2003

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Peaks in the Hartle–Hawking wavefunction from sums over topologies

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