$R^2$/Higgs inflation and the hierarchy problem

TL;DR

This paper examines how $R^2$ and Higgs inflation models address the hierarchy problem, focusing on radiative corrections, fine tuning, and potential observational signatures like gravitational waves and dark matter constraints.

Contribution

It introduces a scale invariant extension of the $R^2$/Higgs inflation model that reduces fine tuning requirements and analyzes its implications for vacuum stability, reheating, and dark matter.

Findings

Fine tuning is reduced to 1 part in 10^{3-4} in the scale invariant model.

The model predicts possible gravitational wave signals from inflation.

Constraints on dark matter mass from gravitational couplings are discussed.

Abstract

We analyse Starobinsky inflation in the presence of the Brout Englert Higgs (BEH) boson with a non-minimal coupling to the Ricci scalar, $R$. The latter induces a coupling of the massive scaleron associated with the $R^2$ term to the BEH boson and this leads to a radiative correction to the BEH mass that must be fine tuned to keep the scalar light. For the case of $R^2$ driven inflation this requires a high level of fine tuning of order 1 part in $10^{8}$; for the case of Higgs inflation it is very much greater. We consider a scale invariant extension of the $R^2$/Higgs model and find that for $R^2$ driven inflation but not for Higgs inflation the required fine tuning is significantly reduced to one part in $10^{3-4}$. We consider the vacuum stability of the fine tuned model and its reheating and dilaton abundance after inflation. We also discuss possible gravitational wave signals associated with the model and the constraint on the mass of scalar or fermion dark matter candidates if they are produced by the gravitational couplings of the scalaron.