Converting non-relativistic dark matter to radiation

TL;DR

This work tests the robustness of the standard DM constancy assumption by allowing a model-independent DM to DR conversion at any epoch after BBN, encoded through a step-like transition with parameters a_t, κ, and ζ. By modifying the background and perturbation evolution, and confronting CMB and LSS data with both Bayesian and frequentist analyses, the authors derive strong CMB constraints on late conversions while showing that late-time DM→DR transitions can modestly relieve CMB–LSS tensions. They map these generic results onto a concrete Sommerfeld-enhanced DM annihilation scenario, identifying a viable TeV-scale, high-n resonance region that yields sizable DM self-interactions and can address small-scale structure problems. Overall, the paper provides a comprehensive framework to test hidden sector DM conversions with cosmological data and highlights how such conversions could reconcile large- and small-scale observational tensions.

Abstract

Dark matter in the cosmological concordance model is parameterised by a single number, describing the covariantly conserved energy density of a non-relativistic fluid. Here we test this assumption in a model-independent and conservative way by considering the possibility that, at any point during the cosmological evolution, dark matter may be converted into a non-interacting form of radiation. This scenario encompasses, but is more general than, the cases where dark matter decays or annihilates into these states. We show that observations of the cosmic microwave background allow to strongly constrain this scenario for any conversion time after big bang nucleosynthesis. We discuss in detail, both from a Bayesian and frequentist point of view, in which sense adding large-scale structure observations may even provide a certain preference for a conversion of dark matter to radiation at late times. Finally we apply our general results to a specific particle physics realisation of such a scenario, featuring late kinetic decoupling and Sommerfeld-enhanced dark matter annihilation. We identify a small part of parameter space that both mitigates the tension between cosmic microwave and large-scale structure data and allows for velocity-dependent dark matter self-interactions strong enough to address the small-scale problems of structure formation.

Figures (15)

• Figure 1: Left panel. Evolution of comoving DM density for the step-like transition described by Eq. (\ref{['rhodmeq']}), for a transition redshift of $a_t=10^{-3}$, a conversion factor of $1+\zeta=1.1$ and, as indicated, four values of the parameter $\kappa$ characterising the steepness of the transition. For comparison, we also show the case of decaying DM (dotted line), assuming that a fraction $\zeta/(1+\zeta)$ of the initial DM abundance decays with a rate $\Gamma= 0.15 H_{\rm eq}$. Right panel. Resulting evolution of the comoving DR density as given in Eq. (\ref{['rhodreq']}). This assumes that there is no additional (e.g. constant) source of DR and, for the translation to $\Delta \tilde{N}_{\rm eff}$ as defined in Eq. (\ref{['eg:neff']}), we have here chosen $\rho_\chi^0$ to agree with the value of $\Omega_\chi^0 h^2=0.1198$ measured by Planck.
• Figure 2: Left panel. Evolution of Hubble rate for the same scenarios as shown in Fig. \ref{['rhodmfig']}, compared to the $\Lambda$CDM Hubble rate $H^{\zeta=0}$ (which in our scenarios is obtained for $\zeta=0$), Right panel. Impact of changing $a_t$ on the Hubble rate, for $\kappa=2$. Orange (thinner) lines indicate the impact of the produced DR alone. For the $a_t=5\cdot 10^{-6}$ case we show, for comparison, also how the Hubble rate is affected by a constant DR contribution, characterised by a constant $\Delta N_{\rm eff}$ (black dotted line).
• Figure 3: Lensed TT spectra for transition rates of $\kappa=2$ (green) and $\kappa=1/2$ (orange) for three different transition times $a_t=5 \cdot 10^{-6}$, $5 \cdot 10^{-4}$, $5 \cdot 10^{-2}$ for fixed $\Lambda$CDM parameters (left) and for the respective best-fit points (right). For comparison we show the $\Lambda$CDM spectrum (solid black line) as well as $\Lambda$CDM $+ \Delta N_\text{eff}$ (dashed black line) for comparison with the early transition case. In the bottom panels we show the fractional difference between the different scenarios and the $\Lambda$CDM case. See text for the remaining parameter values of the models used to obtain these spectra.
• Figure 4: Marginalised 1D posterior pdfs for $\Delta \tilde{N}_{\text{eff}}(a_{\text{rec}})$, normalised such that the maximum value is 1, using the CMB dataset only. The solid lines are for $\kappa=0.5,1,2,4$ with fixed $a_t=10^{-7}$. Note that for $\kappa=2,4$, but not for smaller values of $\kappa$, we have $\Delta \tilde{N}_{\text{eff}}(a_{\text{rec}})=\Delta \tilde{N}_{\text{eff}}^{\rm today}$, cf. Fig. \ref{['rhodmfig']}. For comparison, we also include the standard case of a constant $\Delta N_{\text{eff}} \geq 0$ (dashed black line). The vertical lines indicate the corresponding 95% C.L. limits. For a constant $\Delta N_{\text{eff}}$, our limit is in good agreement with the Planck limit of $0.35$Ade:2015xua (obtained with a flat prior on $\Delta N_{\rm eff}$ that, unlike in our case, also allows $\Delta N_{\rm eff}<0$).
• Figure 5: 95% C.L. (dotted lines) and 99% C.L. (solid lines) Bayesian limits from CMB only; the coloured region above each line is excluded. Left panel. Constraints on the amount of converted DM, cf. Eq. (\ref{['rhodmeq']}). Right panel. Constraints on the amount of DR today, expressed in terms of $\Delta \tilde{N}_{\rm eff}$ as given in Eq. (\ref{['eg:neff']}). For both cases, we adopted a flat prior on $\Delta N_{\rm eff}^{\rm today}$ for $a_t<10^{-4}$, and a flat prior on $\zeta$ for $a_t>10^{-4}$.