Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-10-11
Phys.Rev. D74 (2006) 024023
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, 11 figures
Scientific paper
10.1103/PhysRevD.74.024023
Although the observed universe appears to be geometrically flat, it could have one of 18 global topologies. A constant-time slice of the spacetime manifold could be a torus, Mobius strip, Klein bottle, or others. This global topology of the universe imposes boundary conditions on quantum fields and affects the vacuum energy density via Casimir effect. In a spacetime with such a nontrivial topology, the vacuum energy density is shifted from its value in a simply-connected spacetime. In this paper, the vacuum expectation value of the stress-energy tensor for a massless scalar field is calculated in all 17 multiply-connected, flat and homogeneous spacetimes with different global topologies. It is found that the vacuum energy density is lowered relative to the Minkowski vacuum level in all spacetimes and that the stress-energy tensor becomes position-dependent in spacetimes that involve reflections and rotations.
Sutter Paul M.
Tanaka Tsunefumi
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