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(phi)greater than or similar to 100 eV or a relaxion decay constant f less than or similar to 10(7) GeV is excluded by existing constraints. There is an interesting parameter region with m(phi)similar to 0.2-10GeV and integral similar to few - 200TeV, 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.