Unified Emergence of Energy Scales and Cosmic Inflation

Abstract

In the quest for unification of the Standard Model with gravity, classical scale invariance can be utilized to dynamically generate the Planck mass $M_\mathrm{Pl}$. Then, the relation of Planck scale physics to the scale of electroweak symmetry breaking $\mu_H$ requires further explanation. In this paper, we propose a model that uses the spontaneous breaking of scale invariance in the scalar sector as a unified origin for dynamical generation of both scales. Using the Gildener-Weinberg approximation, only one scalar acquires a vacuum expectation value of $v_S \sim (10^{16-17})\,\mathrm{GeV}$, thus radiatively generating $M_\mathrm{Pl} \approx \beta_S^{1/2} v_S$ and $\mu_H$ via the neutrino option with right handed neutrino masses $m_N = y_M v_S \sim 10^7 \,\mathrm{GeV}$. Consequently, active SM neutrinos are given a mass with the inclusion of a type-I seesaw mechanism. Furthermore, we adopt an unbroken $Z_2$ symmetry and a $Z_2$-odd set of right-handed Majorana neutrinos $\chi$ that do not take part in the neutrino option and are able to produce the correct dark matter relic abundance (dominantly) via inflaton decay. The model also describes cosmic inflation and the inflationary CMB observables are predicted to interpolate between those of $R^2$ and linear chaotic inflationary model and are thus well within the strongest experimental constraints.