Can WIMPs survive the legacy of a magnetised early Universe?

Primordial magnetic fields (PMFs) can seed additional small-scale matter fluctuations, leading to the formation of dense, early-collapsing dark matter structures known as minihalos. These minihalos may dramatically amplify the dark matter annihilation signal if dark matter is composed of self-annihilating thermal relic particles such as WIMPs. In this work, we analyse the annihilation signal from minihalos with prompt central cusps, \rho \propto r^{-3/2} ρ ∝ r − 3 / 2 , formed due to the enhanced power spectrum induced by PMFs, using gamma-ray observations of the Virgo cluster. We consider benchmarks motivated by cosmological phase transitions, focusing in particular on the electroweak and QCD transitions, where we assume maximal magnetic energy density and horizon-sized coherence length at generation (upper-limit scenarios). In addition, we include a data-driven case corresponding to the best-fit present-day PMF amplitude inferred from DESI BAO and Planck CMB measurements. Under these assumptions, we find that PMFs can place stringent bounds on WIMP annihilation. Magnetic fields with amplitudes matching the DESI–Planck best-fit values are in strong tension with self-annihilating WIMPs across a wide mass range extending beyond the () scale, while the electroweak- and QCD-phase-transition toy-model benchmarks would exclude thermal relics with masses below 300\,\mathrm{GeV} 300 G e V and 3\,\mathrm{TeV} 3 T e V , respectively. Although weaker PMFs would yield weaker annihilation signals, our results demonstrate that whenever PMFs enhance small-scale structure, indirect-detection limits on dark matter must be revisited.