No room for minimal monopole dark matter

The magnetic monopole of a dark sector has been advocated as an appealing dark matter candidate. We revisit the computation of the monopole abundance Ω M , generated by a thermal phase transition in the minimal ’t Hooft-Polyakov model. We explore the three regimes where the phase transition is second order, weakly first order, or supercooled, identifying the parameter space regions where Ω M can match the observed dark matter abundance. However, the dark sector necessarily contains a stable electrically charged particle, namely a massive vector boson, with a calculable abundance Ω W ′ . We show that, under minimal assumptions, Ω W ′ is always far larger than Ω M : dark monopoles cannot constitute a sizeable fraction of dark matter.