Vacuum Energy Density for Massless Scalar Fields in Flat Homogeneous Spacetime Manifolds with Nontrivial Topology

摘要

Although the observed universe appears to be geometrically flat, it couldhave one of 18 global topologies. A constant-time slice of the spacetimemanifold could be a torus, Mobius strip, Klein bottle, or others. This globaltopology of the universe imposes boundary conditions on quantum fields andaffects the vacuum energy density via Casimir effect. In a spacetime with sucha nontrivial topology, the vacuum energy density is shifted from its value in asimply-connected spacetime. In this paper, the vacuum expectation value of thestress-energy tensor for a massless scalar field is calculated in all 17multiply-connected, flat and homogeneous spacetimes with different globaltopologies. It is found that the vacuum energy density is lowered relative tothe Minkowski vacuum level in all spacetimes and that the stress-energy tensorbecomes position-dependent in spacetimes that involve reflections androtations.