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Dominant Topologies in Euclidean Quantum Gravity

S. Carlip
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Abstract

The dominant topologies in the Euclidean path integral for quantum gravity differ sharply according on the sign of the cosmological constant. For $Λ>0$, saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For $Λ<0$, 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 $Λ=0$ 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 wave function.

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S. Carlip. 1998-03-23. Dominant Topologies in Euclidean Quantum Gravity. https://doi.org/10.1088/0264-9381%2F15%2F9%2F010

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