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 $m_\phi\gtrsim 100$ eV or a relaxion
decay constant $f\lesssim 10^7$ GeV is excluded by existing constraints. There
is an interesting parameter region with $m_\phi\sim \,0.2-10$ GeV and $f\sim\,
{\rm few}-200$ 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.
