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We show that the Kontsevich-Segal (KS) criterion, applied to the complexsaddles that specify the semiclassical no-boundary wave function, acts as aselection mechanism on inflationary scalar field potentials. Completing theobservable phase of slow-roll inflation with a no-boundary origin, the KScriterion effectively bounds the tensor-to-scalar ratio of cosmic microwavebackground fluctuations to be less than 0.08, in line with currentobservations. We trace the failure of complex saddles to meet the KS criterionto the development of a tachyon in their spectrum of perturbations.

The Kontsevich-Segal Criterion in the No-Boundary State Constrains Inflation