Can WIMPs Survive the Legacy of a Magnetised Early Universe?

TL;DR

The paper investigates how primordial magnetic fields (PMFs) imprint small-scale dark matter structure, creating minihalos with prompt cusps that boost WIMP annihilation signals. It develops a framework linking PMF evolution (turbulent inverse cascade and viscous damping) to the enhanced DM power spectrum and uses BBKS peak statistics to predict prompt cusp populations, then computes the gamma-ray J-factor for the Virgo cluster including cusps. By comparing to gamma-ray limits for annihilation into the $b\bar{b}$ channel, the study derives upper bounds on the annihilation cross section, finding that PMFs can exclude thermal relic WIMPs over a broad mass range, with phase-transition benchmarks excluding $m_χ \lesssim 3$ TeV (QCD-PT) and $m_χ \lesssim 300$ GeV (EW-PT), while a DESI–Planck best-fit PMF strength already imposes tension beyond the TeV scale. The results demonstrate a direct link between early-universe magnetogenesis and indirect detection, showing that PMF-induced small-scale structure can dramatically tighten WIMP constraints and motivate revisiting DM limits when PMFs are present.

Abstract

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, $ρ\propto r^{-3/2}$, 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 TeV scale, while the electroweak- and QCD-phase-transition toy-model benchmarks would exclude thermal relics with masses below $300\,\mathrm{GeV}$ and $3\,\mathrm{TeV}$, 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.

Figures (5)

• Figure 1: Upper limits on the dark matter annihilation cross-section to a $b \bar{b}$ final state in the Virgo cluster, considering a primordial magnetic field with present strength $B_0 = 3.4 \, \mathrm{pG}$, corresponding to the best fit value from the combination of Planck CMB data and the baryon acoustic oscillation (BAO) measurements from the DESI Year 1 release Jedamzik:2025cax. Our limits rule out the thermal annihilation cross-section (black dashed) for dark matter masses extending beyond the $\mathrm{TeV}$ scale. The curve labelled "$\Lambda$CDM" corresponds to $\Lambda$CDM cosmology with self-anihilating dark matter but without any enhancement from primordial magnetic fields, while the B$\Lambda$CDM curve include the additional prompt cusps seeded by PMFs. For the assumptions on the evolution of the magnetic field strength and coherence length, see Sec. \ref{['sec:PMFandHaloFor']}.
• Figure 2: Upper limits on the dark matter annihilation cross-section to a $b\bar{b}$ final state in the Virgo cluster, assuming a primordial magnetic field generated at the QCD phase transition (QCD-PT, red) or at the electroweak phase transition (EW-PT, green dashed). The $\Lambda$CDM baseline with self-annihilating dark matter (blue dotted) and the canonical thermal cross-section (black dashed) are shown for comparison. The QCD-PT scenario yields the strongest bounds, ruling out thermal WIMPs up to multi-TeV masses.
• Figure 3: Cosmological evolution of the comoving magnetic field and relevant comoving length scales for a field generated at an electroweak–scale phase transition with $T_{\rm PT}=160\,\mathrm{GeV}$. Top:$B_{\rm com}(a)$ (solid) with a turbulent guide $B\propto a^{-10/17}$ (dashed). Bottom: Coherence length $\xi=1/k$ (black) alongside neutrino diffusion $\ell_{\nu D}$ (purple), horizon $R_H=(aH)^{-1}$ (blue), photon diffusion $\ell_{\gamma D}$ (orange), photon mean free path $\ell_{\gamma\rm mfp}$ (orange, dashed), and the baryon thermal–pressure scale $\ell_{\rm Baryon}$ (red). Vertical lines mark $a_I$ and $a_{\rm rec}$. PMFs evolve under viscous damping when $\xi$ is below the relevant diffusion/free–streaming scales.
• Figure 4: Lower bound on the temperature of the phase transition $T_{\rm PT}$ as a function of the dark matter mass $m_{\rm DM}$, assuming that the magnetic energy density at generation equals that of the Standard Model plasma. The evolution of the magnetic field strength and coherence length is given in Sec. \ref{['sec:PMFandHaloFor']}. For a given dark matter mass, values of $T_{\rm PT}$ below the curve are excluded under the assumption of thermal-relic annihilation.
• Figure 5: Scaling of the predicted annihilation $J$–factor with (a) the present-day PMF strength $B_{0}$ and (b) the present-day coherence length $\xi_{0}$. The results correspond to the Virgo cluster, assuming a dark-matter mass of $m_{\rm DM}=100~\mathrm{GeV}$ and a kinetic-decoupling temperature of $T_{\rm kd}=30~\mathrm{GeV}$.