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

TL;DR

This paper calculates the vacuum energy density for massless scalar fields in 17 different flat, homogeneous spacetimes with nontrivial topologies, revealing topology-dependent shifts and position dependence of the vacuum energy.

Contribution

It provides explicit calculations of the vacuum expectation value of the stress-energy tensor for all 17 multiply-connected flat topologies, extending understanding of quantum field effects in complex universe models.

Findings

Vacuum energy density is lowered in all studied topologies.

Stress-energy tensor varies with position in certain topologies.

Topological features influence quantum vacuum properties.

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, 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.