Vacuum energy density for massless scalar fields in flat homogeneous spacetime manifolds with nontrivial topology
Year: 2006
Type: article
Abstract: 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, M\"obius strip, Klein bottle, or others. This global topology of the universe imposes boundary conditions on quantum fields and affects the vacuum energy density via the 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.
Authors: P. M. Sutter, Tsunefumi Tanaka
Institution: California Polytechnic State University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1981164378