No-Boundary Theta-Sectors in Spatially Flat Quantum Cosmology

TL;DR

This paper explores gravitational theta-sectors in spatially flat quantum cosmology, revealing that nontrivial sectors with a no-boundary wave function exist only in 3+1 dimensions for specific nonorientable topologies.

Contribution

It demonstrates the existence and uniqueness of nontrivial no-boundary theta-sectors in 3+1 dimensions with nonorientable spatial surfaces, and clarifies their topological origin in 2+1 dimensions.

Findings

Nontrivial theta-sectors exist only in 3+1 dimensions.

Such sectors are associated with nonorientable spatial surfaces.

The nonexistence in 2+1 dimensions is topologically rooted.

Abstract

Gravitational theta-sectors are investigated in spatially locally homogeneous cosmological models with flat closed spatial surfaces in 2+1 and 3+1 spacetime dimensions. The metric ansatz is kept in its most general form compatible with Hamiltonian minisuperspace dynamics. Nontrivial theta-sectors admitting a semiclassical no-boundary wave function are shown to exist only in 3+1 dimensions, and there only for two spatial topologies. In both cases the spatial surface is nonorientable and the nontrivial no-boundary theta-sector unique. In 2+1 dimensions the nonexistence of nontrivial no-boundary theta-sectors is shown to be of topological origin and thus to transcend both the semiclassical approximation and the minisuperspace ansatz. Relation to the necessary condition given by Hartle and Witt for the existence of no-boundary theta-states is discussed.