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Dominant topologies in Euclidean quantum gravity

S Carlip

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The dominant topologies in the Euclidean path integral for quantum gravity differ sharply according to the sign of the cosmological constant. For , saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For , on the other hand, the path integral is dominated by topologies with extremely complicated fundamental groups; while the contribution of each individual manifold is strongly suppressed, the `density of topologies' grows fast enough to overwhelm this suppression. The value is thus a sort of boundary between phases in the sum over topologies. I discuss some implications for the cosmological constant problem and the Hartle-Hawking wavefunction.


PACS

04.60.-m Quantum gravity

02.40.-k Geometry, differential geometry, and topology

98.80.Es Observational cosmology (including Hubble constant, distance scale, cosmological constant, early Universe, etc)

MSC

83F05 Cosmology

83Cxx General relativity

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)

Subjects

Mathematical physics

Gravitation and cosmology

Astrophysics and astroparticles

Dates

Issue 9 (September 1998)

Received 28 October 1997



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