Planck mass and inflation as consequences of dynamically broken scale invariance

Abstract

Classical scale invariance represents a promising framework for model building beyond the Standard Model. However, once coupled to gravity, any scale-invariant microscopic model requires an explanation for the origin of the Planck mass. In this paper, we provide a minimal example for such a mechanism and show how the Planck mass can be dynamically generated in a strongly coupled gauge sector. We consider the case of hidden $SU({N}_{c})$ gauge interactions that link the Planck mass to the condensation of a scalar bilinear operator that is nonminimally coupled to curvature. The effective theory at energies below the Planck mass contains two scalar fields: the pseudo--Nambu-Goldstone boson of spontaneously broken scale invariance (the dilaton) and a gravitational scalar degree of freedom that originates from the ${R}^{2}$ term in the effective action (the scalaron). We compute the effective potential for the coupled dilaton-scalaron system at one-loop order and demonstrate that it can be used to successfully realize a stage of slow-roll inflation in the early Universe. Remarkably enough, our predictions for the primordial scalar and tensor power spectra interpolate between those of standard ${R}^{2}$ inflation and linear chaotic inflation. For comparatively small gravitational couplings, we thus obtain a spectral index ${n}_{s}\ensuremath{\simeq}0.97$ and a tensor-to-scalar ratio as large as $r\ensuremath{\simeq}0.08$.