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Steve Carlip - Einstein manifolds, spacetime foam, and the cosmological constant
| STEVE CARLIP, Department of Physics, University of California at Davis, Davis, California 95616, USA | |
| Einstein manifolds, spacetime foam, and the cosmological constant |
In Wheeler's ``spacetime foam'' model, the quantum mechanical state of
the universe is a superposition of many different spacetime
topologies. In a saddle point approximation for the partition
function, each Einstein manifold M contributes a term of the form
, where 
is the cosmological
constant and 
is the volume of M with scalar curvature
normalized to 
. For 
, one therefore naively expects
the sum over topologies to be dominated by a few manifolds with small
volumes. Contrary to this expectation, I show that the number of
hyperbolic manifolds grows so fast with volume that the sum over
topologies is dominated by arbitrarily large manifolds with arbitrarily
complicated topologies. This phenomenon indicates an instability in
the sum over topologies that may be relevant to the ``cosmological
constant problem,'' the observation that the vacuum energy density of
the universe is at least 120 orders of magnitude smaller than one
would expect from quantum fluctuations at the Planck scale. Processes
that would normally increase 
may instead merely drive the
production of more and more complicated spacetime foam.
Next: Lisa Jeffrey - Holomorphic Up: Low Dimensional Topology / Previous: John M. Bryden - eo@camel.math.ca
