No room for 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 $\Omega_M$, 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 $\Omega_M$ 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 $\Omega_{W'}$. We show that, under minimal assumptions, $\Omega_{W'}$ is always far larger than $\Omega_M$: dark monopoles cannot constitute a sizeable fraction of dark matter.