Phenomenological effects of non-toroidal Euclidean topologies

Determine how the shape parameters and compactification scales of the nontrivial Euclidean spatial topologies E2 through E17 affect early-Universe de Sitter dynamics and whether their topology-dependent vacuum contributions can generate phenomenologically relevant effects at late times.

Background

The explicit calculations in the paper use the three-torus, E1, as a tractable example. The authors argue that the mechanism should extend to the other nontrivial Euclidean topologies because their global identifications likewise reduce the symmetry of the simply connected covering space.

Those topologies possess additional shape parameters and potentially very different compactification scales, which can modify the Casimir contribution and the resulting vacuum stress tensor. The impact of this enlarged parameter space on inflationary dynamics and late-time vacuum energy remains unresolved.