Reannihilation of self-interacting dark matter

TL;DR

This paper investigates a second epoch of dark matter annihilation into dark radiation—reannihilation—in self-interacting dark matter models with a light mediator in a closed dark sector. It shows that Sommerfeld-enhanced, $s$-wave annihilation in vector-mediator scenarios can drive a temporally localized depletion of DM after kinetic decoupling, modifying the Hubble expansion and leaving imprints on the CMB. Through analytic estimates and coupled Boltzmann-Hubble equations, the authors map the viable parameter space, demonstrate potential alleviation of the $H_0$ and $σ_8$ tensions, and propose a distinctive signature to distinguish vector from scalar mediators. They emphasize the necessity of a dedicated Boltzmann code to accurately capture perturbation-level signatures and CMB constraints on reannihilation scenarios.

Abstract

We explore the phenomenology of having a second epoch of dark matter annihilation into dark radiation long after the standard thermal freeze-out. Such a hidden reannihilation process could affect visible sectors only gravitationally. As a concrete realization we consider self-interacting dark matter (SIDM) with a light force mediator coupled to dark radiation. We demonstrate how resonantly Sommerfeld enhanced cross sections emerge to induce the reannihilation epoch. The effect is a temporally local modification of the Hubble expansion rate and we show that the Cosmic Microwave Background (CMB) measurements -- as well as other observations -- have a high sensitivity to observe this phenomenon. Special attention is given to the model region where late kinetic decoupling and strong self-interactions can alleviate several small-scale problems in the cold dark matter paradigm at the same time. Interestingly, we find that reannihilation might here also simultaneously lower the tension between CMB and low-redshift astronomical observations of $H_{0}$ and $σ_{8}$. Moreover, we identify reannihilation as a clear signature to discriminate between the phenomenologically otherwise almost identical vector and scalar mediator realizations of SIDM.

Figures (9)

• Figure 1: Reannihilation process shown as a function of $x\equiv m_{\chi} /T_{\gamma}$, changing the DM co-moving number density $Y\equiv n_{\chi}/s$ by one order of magnitude. The final abundance coincides with the correct value (black horizontal line). Here, we have chosen the parameters $m_{\chi} = 1 \, \text{TeV}$, $\alpha_{\chi} = 0.007$, $m_{\phi} \simeq 1 \, \text{GeV}$ and the resonance number $n \simeq 2$ (where $m_{\phi}$ is tuned to get the correct relic density). Between the gray solid lines kinetic decoupling happens and the scaling of the DM temperature changes from $T_{\chi} \propto T$ to $T_{\chi} \propto T^{2}$. The dashed gray line indicates the start of reannihilation, where velocity-dependent annihilation lead to deviation from the $T_{\chi} \propto T^{2}$ scaling.
• Figure 2: Time evolution of the DM abundance $Y \equiv n_{\chi} / s$, its temperature $y \equiv \frac{m_{\chi}}{s^{2/3}} T_{\chi}$ and its phase-space density $f(q)$ with $q = p / T_{\gamma}$. Left panel: The evolution of $Y$ (blue) and $y$ (yellow) in the case of strongly self-interacting DM (dotted lines) and in the case of no DM self-interactions (solid). Right panel: Unit normalized phase-space distributions $f_{n} (q)$ from our full numerical solution of the Boltzmann equation (red lines) compared to thermal equilibrium distributions $f^{\text{eq}}_{n} (q)$ with the same "temperature" $T_{\chi}$ (blue lines). The phase-space distributions are shown at four different $x \simeq$$10^{6}$ (solid), $10^{8}$ (dashed), $10^{9}$ (dot-dashed) and $10^{10}$ (dotted). The bottom panel shows the ratio $f_{n} (q) / f_{n}^{\text{eq}} (q)$. The DM model is $m_{\chi} = 600$ GeV, $m_{\phi} \simeq 1$ GeV and $\alpha_{\chi}$ chosen such that the relic abundance retains the observed DM abundance after the reannihilation period. Both plot styles are chosen to resemble those in Ref. Binder:2017rgn.
• Figure 3: Relic abundance ratio shown vs. the coupling $\alpha_{\chi}$ for fixed $m_{\chi}=1$ TeV and $m_{\phi}=10$ MeV. Dashed black curve is the result for only taking the standard thermal freeze-out into account (labelled as off resonance). The red dots present points where the parametric resonance condition is exactly fulfilled and reannihilation thus lowers the relic abundance maximally. Moving left or right from an exact resonance point by changing $\alpha_{\chi}$ slightly can lead to $(\Omega_{\chi} h^{2})/(\Omega_{c} h^{2})_{\text{Planck}} = 1$ but only for the red points that cross the horizontal black line. The relic abundance is therefore degenerate in these (almost) on resonance $\alpha_{\chi}$ values.
• Figure 4: Number of Sommerfeld resonances, color-coded as given in the top panel, leading to the correct relic density today and changing the co-moving DM number density by at least $1 \, \%$ during the epoch of reannihilation. The red solid lines show our analytic estimates (see Appendix \ref{['app:softrea']}) of the border where reannihilation can change the relic abundance at most by $1 \, \%$ and $10 \, \%$. In the shaded grey area in the bottom right part of the figure, no resonances are available leading to the correct relic density. Brown shaded area represents the estimated region where reannihilation cannot proceed after matter-radiation equality. Blue and light blue shaded areas cover the parameter space where DM has a sizable self-scattering cross section on dwarf galactic scales: $(\sigma_{T})_{30 \, \text{km/s}}/m_{\chi} \in [0.1,10] \, \text{cm}^{2} \text{g}^{-1}$. The "proper" SIDM region, both in the quantum-resonant and classical self-scattering regime, overlaps with the parameter space where sizable reannihilation can occur. In the quantum-resonant regime, $\alpha_{\chi}$ is adjusted in the computation of $\sigma_{T}$ such that for given $m_{\chi}$ and $m_{\phi}$ the resonance condition, $\epsilon_{\phi} = 6/(n^{2} \pi^{2})$, is fulfilled for a given integer $n$ (see last subsection of Section \ref{['sec:analysis']} for a detailed explanation). For comparison, the black dashed self-scattering band is for $\alpha_{\chi}$ satisfying the relic density constraint without taking reannihilation or resonances into account. Cutoff masses of the order of $10^{7}$, $10^{8}$, and $10^{9} \, M_{\odot}$ in the halo-mass function are represented by the purple lines. In the stripe between the green lines, reannihilation induces the first decrease of the DM co-moving number density by $1\, \%$ between redshifts of $z = 300$ and $z= 1000$ --- while the maximal change in the DM abundance can be read off from the red lines. In the parameter space where the blue region, the green lines and the purple lines all overlap, SIDM could at the same time alleviate several small-scale structure formation problems and tensions between cosmological parameters derived from CMB and low-redshift astronomical observations (see Section \ref{['sec:cosmogeneral']} and Fig. \ref{['fig:handdars']}).
• Figure 5: Evolution of the DM number density $Y = n_{\chi} / s$ (blue line) and the corresponding expansion rate $H$ (yellow line) shown as a function of the redshift. The onset ($1 \, \%$ change in $Y$) of reannihilation for the dashed and solid curves is around $z \simeq 3 \times 10^{4}$ and the DM abundance is initially enhanced by 3 and $5 \, \%$, respectively. The final relic abundances coincide with $(\Omega_{c} h^{2})_{\text{Planck}} = 0.1197$ and the ratio $H / H_{\text{Planck}}$ therefore reaches 1 at low redshifts. Both scenarios would be in strong tension with the observed value of $100 \theta_{*}$, see Fig. \ref{['fig:sigma']}.