WIMPs and new physics interpretations of the PTA signal are incompatible

In order to explain the large amplitude of the nano-Hertz stochastic gravitational wave background observed in pulsar timing arrays (PTA), primordial sources must be particularly energetic. This is correlated to the generation of large density fluctuations, later collapsing into ultra-compact mini-halo (UCMHs). We demonstrate that if dark matter is made of WIMPs, then photon and neutrino fluxes from UCMHs produced by curvature peaks, first-order phase transition and domain wall interpretations of the PTA signal, exceed current bounds.