Kontsevich-Segal criterion in the no-boundary state constrains anisotropy

We show that the Kontsevich-Segal-Witten (KSW) criterion applied to the no-boundary state constrains anisotropic deformations of de Sitter space. We consider squashed S3 and S1×S2 boundaries and find that, in both models, the KSW criterion excludes a significant range of homogeneous but anisotropic configurations. For squashed S3 boundaries, the excluded range includes all surface geometries with negative scalar curvature, in line with dS/CFT reasoning. For S1×S2 boundaries, we find that KSW selects the low-temperature regime of configuration space where the S1 is sufficiently large compared to the S2. In both models, the KSW criterion renders the semiclassical wave function normalizable, up to one-loop effects.