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 ${\mathrm{\Omega }}_M$, 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 ${\mathrm{\Omega }}_M$ 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 ${\mathrm{\Omega }}_{W^{\mathrm{\prime }}}$. We show that, under minimal assumptions, ${\mathrm{\Omega }}_{W^{\mathrm{\prime }}}$ is always far larger than ${\mathrm{\Omega }}_M$: dark monopoles cannot constitute a sizeable fraction of dark matter.