Relic density and CMB constraints on dark matter annihilation with Sommerfeld enhancement

TL;DR

This work investigates how Sommerfeld enhancement, arising from a Yukawa-mediated attractive force between dark matter particles, alters the relic density and potentially leaves imprints on the cosmic microwave background. By solving the Schrödinger equation for the boost factor $S$ and incorporating it into the Boltzmann treatment with kinetic decoupling, the authors find that the relic density is suppressed relative to the standard case, requiring a substantial downward normalization of the cross section $\langle\sigma v\rangle_S$ (up to about an order of magnitude near resonances) to match the observed abundance $\Omega_\chi h^2 \approx 0.114$. They also compute the $\mu$-type distortion of the CMB caused by energy injection from Sommerfeld-enhanced annihilation and show that near resonances the distortion can exceed COBE/FIRAS limits, with even stronger exclusions in the Coulomb limit where $\alpha_c$ above a few $\times 10^{-2}$ is ruled out. The results imply that boosts proposed to explain cosmic-ray anomalies must be recalibrated against both relic-density constraints and CMB distortions, and they provide a public tool to evaluate these quantities for given model parameters.

Abstract

We calculate how the relic density of dark matter particles is altered when their annihilation is enhanced by the Sommerfeld mechanism due to a Yukawa interaction between the annihilating particles. Maintaining a dark matter abundance consistent with current observational bounds requires the normalization of the s-wave annihilation cross section to be decreased compared to a model without enhancement. The level of suppression depends on the specific parameters of the particle model, with the kinetic decoupling temperature having the most effect. We find that the cross section can be reduced by as much as an order of magnitude for extreme cases. We also compute the mu-type distortion of the CMB energy spectrum caused by energy injection from such Sommerfeld-enhanced annihilation. Our results indicate that in the vicinity of resonances, associated with bound states, distortions can be large enough to be excluded by the upper limit |mu|<9.0x10^(-5) found by the COBE/FIRAS experiment.

Figures (6)

• Figure 1: Values of the normalization of the thermally averaged cross section $\left<\sigma v\right>_S$ that give the proper relic density $\Omega_{\chi}h^2=0.1143$ in the parameter space ($m_{\phi}/m_{\chi}$, $\alpha_c$) for $m_{\chi}=100~{\rm GeV}$ and $T_{kd}=8$ MeV. The values are given in a color scale shown on the right hand side in units of $1\times10^{-26}{\rm cm^3 s^{-1}}$.
• Figure 2: Map ratio of the value of the cross section giving the correct relic density $\Omega_{\chi}h^2=0.1143$ with different kinetic decoupling temperatures, $T_{kd}=150$ MeV and $T_{kd}=4$ MeV for a $100$ GeV neutralino.
• Figure 3: Scan of the parameter space ($m_{\phi}/m_{\chi}$, $\alpha_c$) with the expected values of the $\mu$-type distortion to the CMB spectrum for $m_{\chi}=100$ GeV, $T_{kd}=8$ MeV and cross section values satisfying the constraint in the relic density: $\Omega_{\chi}h^2=0.1143$. The $2\sigma$ observational upper limit on $\vert\mu\vert$ is $9\times10^{-5}$. The plot shows the values of the logarithm of $\mu$ color-coded according to the scale on the right.
• Figure 4: The values of the $\mu$ distortion parameter near the first resonance in the upper left corner of Fig. \ref{['mu']} as a function of the perpendicular distance to the resonance. The lines with different colors correspond to different values of $T_{kd}$ and $\Omega_{\chi}h^2$ as marked in the legend. The solid black horizontal line shows the upper limit on $\mu$ according to the COBE/FIRAS experiment. As in Fig. \ref{['mu']}, $m_{\chi}=100$ GeV.
• Figure 5: The same as Fig. \ref{['mu']} but for the case where the interaction is strictly Coulomb-like. We have taken fiducial values of $m_{\chi}=100$ GeV, $T_{kd}=8$ MeV and $\Omega_{\chi}h^2=0.1143$. Values above the black solid horizontal line are excluded by the current limits of $\mu$ according to the COBE/FIRAS experiment.