Relaxion: A Landscape Without Anthropics

TL;DR

The paper explores a relaxion mechanism during inflation that naturally addresses the hierarchy problem, the strong CP problem, and dark matter, by analyzing the axion-like field's behavior at different Hubble scales.

Contribution

It proposes a novel inflationary scenario with a specific Hubble scale range that allows the relaxion to solve multiple fundamental problems simultaneously.

Findings

Relaxion can resolve hierarchy and strong CP problems during inflation.

Hubble scale between weak scale and 3 GeV is optimal for the mechanism.

The model remains technically natural under the proposed conditions.

Abstract

The relaxion mechanism provides a potentially elegant solution to the hierarchy problem without resorting to anthropic or other fine-tuning arguments. This mechanism introduces an axion-like field, dubbed the relaxion, whose expectation value determines the electroweak hierarchy as well as the QCD strong CP violating $\bar{\theta}$ parameter. During an inflationary period, the Higgs mass squared is selected to be negative and hierarchically small in a theory which is consistent with 't Hooft's technical naturalness criteria. However, in the original model proposed by Graham, Kaplan and Rajendran (2015), the relaxion does not solve the strong CP problem, and in fact contributes to it, as the coupling of the relaxion to the Higgs field and the introduction of a linear potential for the relaxion produces large strong CP violation. We resolve this tension by considering inflation with a Hubble scale which is above the QCD scale but below the weak scale, and estimating the Hubble temperature dependence of the axion mass. The relaxion potential is thus very different during inflation than it is today. We find that provided the inflationary Hubble scale is between the weak scale and about 3 GeV, the relaxion resolves the hierarchy, strong CP, and dark matter problems in a way that is technically natural.