Solving the Standard Model Problems in Softened Gravity

Abstract

The Higgs naturalness problem is solved if the growth of Einstein's gravitational interaction is softened at an energy $\lesssim 10^{11}$GeV (softened gravity). We work here within an explicit realization where the Einstein-Hilbert Lagrangian is extended to include terms quadratic in the curvature and a non-minimal coupling with the Higgs. We show that this solution is preserved by adding three right-handed neutrinos with masses below the electroweak scale, accounting for neutrino oscillations, dark matter and the baryon asymmetry. The smallness of the right-handed neutrino masses (compared to the Planck scale) and the QCD $\theta$-term are also shown to be natural. We prove that a possible gravitational source of CP violation cannot spoil the model, thanks to the presence of right-handed neutrinos. Inflation is approximately described by the Starobinsky model in this context, and can occur even if we live in a metastable vacuum.

21 pages, 1 figure; v2: extended version required by Phys.Rev.D

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• Initial Conditions for Critical Higgs Inflation
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