Softly Fine-Tuned Standard Model and the Scale of Inflation

Abstract

The direct coupling between the Higgs field and the spacetime curvature, if finely tuned, is known to stabilize the Higgs boson mass. The fine-tuning is soft because the Standard Model (SM) parameters are subject to no fine-tuning thanks to their independence from the Higgs-curvature coupling. This soft fine-tuning leaves behind a large vacuum energy $\propto \Lambda_{\rm UV}^4$ which inflates the Universe with a Hubble rate $\propto \Lambda_{\rm UV}$, $\Lambda_{\rm UV}$ being the SM ultraviolet boundary. This means that the tensor-to-scalar ratio inferred from cosmic microwave background polarization measurements by BICEP2, Planck and others lead to the determination of $\Lambda_{\rm UV}$. The exit from the inflationary phase, as usual, is accomplished via decays of the vacuum energy. Here we show that, identification of $\Lambda_{\rm UV}$ with the inflaton, as a sliding UV scale upon the SM, respects the soft fine-tuning constraint and does not disrupt the stability of the SM Higgs boson.