Why is the apparent cosmological constant zero?

Abstract

The apparent cosmological constant is measured to be zero with an accuracy greater than that for any other quantity in Physics. On the other hand one would expect a large induced cosmological constant unless the various contributions from symmetry breaking, etc., were balanced against each other to better than 1 part in 10⁴⁰ It is suggested that this puzzle can be resolved by assuming that quantum state of the universe is not chosen at random but contains only states with a very large Euclidean 4-volume. In this situation the actual value of the cosmological constant is unobservable. There are solutions of the Einstein equations with a large cosmological constant which appear nearly flat on large length scales but which are highly curved and topologically complicated on very small length scales. Estimates are made of the spectrum of these topological fluctuations and of their effects on the propagation of particles.