Self-Consistent Parker Bound on Magnetic Monopoles

Magnetic monopoles arise generically in unified theories and offer a natural explanation of charge quantization. Beyond collider searches and cosmic-ray experiments, their flux is constrained by Parker-type bounds requiring galactic magnetic fields to survive monopole energy extraction. We formulate a self-consistent Parker bound anchored in the lowest eigenmode of the galactic mean-field dynamo and convert the resulting limit to the present flux. Small-scale turbulent fields both seed this eigenmode and set the monopole velocity via stochastic acceleration before energy extraction from the coherent field. These unavoidable effects substantially modify the standard extended Parker bound at low and intermediate masses, yielding flux limits robust to primordial magnetic fields (PMFs); PMFs strong enough to alter them lie in regimes constrained by Ly$\alpha$ data or testable by 21-cm and cosmological probes.