Dynamically Induced Planck Scale and Inflation

Abstract

Theories where the Planck scale is dynamically generated from dimensionless interactions provide predictive inflationary potentials and super-Planckian field variations. We first study the minimal single-field realisation in the low-energy effective field theory limit, finding the predictions $n_s \approx 0.96$ for the spectral index and $r \approx 0.13$ for the tensor-to-scalar ratio, which can be reduced down to $\approx 0.04$ in presence of large couplings. Next we consider agravity as a dimensionless quantum gravity theory finding a multi-field inflation that converges towards an attractor trajectory that predicts $n_s\approx 0.96$ and $0.003<r<0.13$, 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 $10^{7-9}$ GeV. A measurement of $r$ by Keck/Bicep3 would give us information on quantum gravity in the dimensionless scenario.