Constraints on relaxion windows

We examine the low energy phenomenology of the relaxion solution to the weak scale hierarchy problem. assuming that the hubble friction is responsible for a dissipation of the relaxion energy, we identify the cosmological relaxion window which corresponds to the parameter region compatible with a given value of the acceptable number of inflationary e-foldings. we then discuss a variety of observational constraints on the relaxion window, including those from astrophysical and cosmological considerations. we find that majority of the parameter space with a relaxion mass m ϕ ≳ 100 ev or a relaxion decay constant f ≲107gev is excluded by existing constraints. there is an interesting parameter region with m ϕ ∼ 0.2 − 10 gev and f ∼ few − 200 tev, which is allowed by existing constraints, but can be probed soon by future beam dump experiments such as the ship experiment, or by improved edm experiments.