ICTS

We consider the recently proposed cosmological relaxation mechanism where the hierarchy problem is ameliorated, and the electroweak scale is dynamically selected by a slowly rolling axion field. We argue that, in its simplest form, the construction breaks a gauge symmetry that always exists for pseudo-Nambu-Goldstone bosons (in particular the axion). An equivalent statement is that for a PNGB of period 2 \pi f all terms in its potential must have this periodicity and the non-periodic rolling potential of the relaxion breaks this requirement. We also consider multi-axion models proposed to address this issue and discuss a new bound on the number of axions in these models, which in turn puts a bound on the cut-off. Apart from this we derive experimental bounds on the relaxion parameter space from high intensity lab probes, cosmological late decays and astrophysics. Together these new theoretical and experimental bounds but a bound on the cut-off in the 10-1000 TeV range and suggest that in the region safest from these constraints the relaxion mass is likely to be within a KeV and a MeV.