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.
