Observable dark radiation from a cosmologically safe QCD axion

We propose a QCD axion model that avoids the cosmological domain wall problem, introducing a global SU(3)f family symmetry in which we embed the unwanted Peccei-Quinn (PQ) discrete symmetry. The spontaneous breaking of SU(3)f and PQ symmetry predicts eight NG bosons as well as axion, all of which contribute to the energy density of the Universe as dark radiation. The deviation from the standard model prediction of dark radiation can be observed by future observations of cosmic microwave background fluctuations. Our model also predicts a sizable exotic kaon decay rate, which is marginally consistent with the present collider data and would be tested by future collider experiments.