Primordial black holes as dark matter through Higgs field criticality
In this work, we study the dynamics of a spectator Higgs field which stochastically evolves during inflation onto near-critical trajectories on the edge of a runaway instability. We show that its fluctuations do not produce primordial black holes in sufficient abundance to be the dark matter, nor do they produce significant second-order gravitational waves. First we show that the Higgs produces larger fluctuations on cosmic microwave background scales than on primordial black hole (PBH) scales, itself a no go for a viable PBH scenario. Then we track the superhorizon perturbations nonlinearly through reheating using the $δ\textit{N}$ formalism to show that they are not converted to large curvature fluctuations. Our conclusions hold regardless of any fine-tuning of the Higgs field for both the Standard Model Higgs and Higgs potentials modified to prevent unbounded runaway.