Fig. 1: Inconsistency of the decay theory based on Equations (6) and (9) with observational constraints for EWPT-generated PMFs.

Purple regions denote values of \(\tilde{B}\) and λ_B excluded on physical [\({\tilde{\rho }}_{B}(t)\, \lesssim \, {\tilde{\rho }}_{\gamma }({t}_{*})\)] or observational [the two forms of the constraint (1)] grounds. Under decays that conserve \({I}_{{{{{{{{{\bf{L}}}}}}}}}_{M}}\) [Equation (4)], \(\tilde{B}\) and λ_B evolve along lines parallel to the ones shown in blue. The predicted values of modern-day \(\tilde{B}\) and λ_B are given by the intersection of these lines with Equation (10). We see that even PMFs generated with \({\tilde{\rho }}_{B}({t}_{*}) \sim {\tilde{\rho }}_{\gamma }({t}_{*})\) and λ_B(t_*) ~ r_H(t_*) produce modern-day relics that are inconsistent with Equation (1).