Relaxing the Electroweak Scale: the Role of Broken dS Symmetry

TL;DR

This paper explores how breaking de Sitter symmetry during inflation can enhance the relaxion mechanism, potentially reducing the required e-folds and cutoff scale, and discusses its implications for cosmology and particle physics.

Contribution

It demonstrates that breaking exact de Sitter invariance allows larger relaxion field excursions with fewer e-folds, impacting the hierarchy problem solution and dark matter models.

Findings

Larger relaxion excursions are possible with broken dS symmetry.

Successful relaxion mechanism can occur with about 1000 e-folds.

Reduced cutoff scale to around 10^6 GeV for dark QCD axion.

Abstract

Recently, a novel mechanism to address the hierarchy problem has been proposed \cite{Graham:2015cka}, where the hierarchy between weak scale physics and any putative `cutoff' $M$ is translated into a parametrically large field excursion for the so-called relaxion field, driving the Higgs mass to values much less than $M$ through cosmological dynamics. In its simplest incarnation, the relaxion mechanism requires nothing beyond the standard model other than an axion (the relaxion field) and an inflaton. In this note, we critically re-examine the requirements for successfully realizing the relaxion mechanism and point out that parametrically larger field excursions can be obtained for a given number of e-folds by simply requiring that the background break exact de Sitter invariance. We discuss several corollaries of this observation, including the interplay between the upper bound on the scale $M$ and the order parameter $\epsilon$ associated with the breaking of dS symmetry, and entertain the possibility that the relaxion could play the role of a curvaton. We find that a successful realization of the mechanism is possible with as few as $\mathcal O (10^3)$ e-foldings, albeit with a reduced cutoff $M \sim 10^6$ GeV for a dark QCD axion and outline a minimal scenario that can be made consistent with CMB observations.