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

Abstract

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

Dedicated to the memory of Jim Hartle

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• A small Universe
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• Conformal Cores of Quantum Black Holes in Quadratic Gravity
• Delicate curvature bounces in the no-boundary wave function and in the late universe
• Complex Saddles of Charged-AdS Gravitational partition function
• Resolving Degeneracies in Complex $\mathbb{R}\times S^3$ and $\theta$-KSW