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

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The Kontsevich-Segal criterion selects inflationary potentials, bounding the tensor-to-scalar ratio from cosmic microwave background fluctuations to below 0.08. This aligns with observations and is linked to tachyonic instabilities in complex saddles.

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Area of Science:

  • Cosmology
  • Theoretical Physics
  • Quantum Gravity

Background:

  • The no-boundary proposal offers a quantum origin for the universe.
  • Inflationary cosmology describes the universe's early rapid expansion.
  • The tensor-to-scalar ratio is a key observable in cosmic microwave background radiation.

Purpose of the Study:

  • To investigate the role of the Kontsevich-Segal (KS) criterion in selecting inflationary models.
  • To connect the KS criterion to the semiclassical no-boundary wave function.
  • To constrain the tensor-to-scalar ratio predicted by inflationary potentials.

Main Methods:

  • Applying the KS criterion to complex saddles of the no-boundary wave function.
  • Analyzing the spectrum of perturbations for tachyonic instabilities.
  • Relating theoretical predictions to observational constraints on the tensor-to-scalar ratio.

Main Results:

  • The KS criterion acts as a selection mechanism for inflationary scalar field potentials.
  • The KS criterion bounds the tensor-to-scalar ratio to be less than 0.08.
  • Failure to meet the KS criterion is associated with the development of a tachyon.

Conclusions:

  • The KS criterion provides a theoretical basis for observed bounds on the tensor-to-scalar ratio.
  • The no-boundary wave function, with KS criterion selection, offers a viable model for early universe cosmology.
  • Tachyonic instabilities signal the breakdown of certain complex saddle solutions in inflationary models.