Dynamically induced planck scale and inflation

Abstract

We present a minimal model of inflation where the Planck scale is dynamically generated from dimensionless interactions. The inflaton field φ gets a vacuum expectation value via dimensional transmutation. The Planck scale is generated via its non-minimal coupling to gravity ζφ2 R. To generate the minimum of the inflaton potential, one needs a singlet scalar and new fermion(s) which can provide a dark matter candidate. The spectral index is predicted to be ns ≈ 0.96. The tensor-to-scalar ratio can vary from r ≈ 0.13 down to r ≈ 0.04 in presence of large couplings or r ≈ 0.003 if the Lagrangian contains an R2 term, interpolating between the quadratic and Starobinsky inflation. These theories relate the smallness of the weak scale to the smallness of inflationary perturbations: both arise naturally because of small couplings, implying a reheating temperature of 107...9 GeV. A measurement of r by Keck/BICEP3 would give us information on quantum gravity in the dimensionless scenario.