Dark Matter-Dark Radiation Interactions and the Hubble Tension

TL;DR

This paper addresses the Hubble tension by testing generalized interacting DM–DR models (gen-iDM) in which a subcomponent of dark matter, $f_ ext{idm}$, stays in thermal contact with dark radiation (parameterized by $\Delta N_ ext{eff}$) and decouples around matter–radiation equality. It explores three decoupling-rate scalings, $\Gamma_d(T) \propto T^{2+n}$ with $n=4,2,0$, mapping to four-fermion, Compton-like, and Coulomb-like interactions, and constrains them using Planck2018, ACT DR6, BAO, LSS, SNIa, and Cepheid data. Without ACT DR6, all three benchmarks alleviate the Hubble tension relative to $\Lambda$CDM, with the fastest decoupling ($n=0$) being the most favored; including SH0ES can push $H_0$ to values that reduce the tension below $1\sigma$, whereas ACT DR6 data tend to weaken or remove these gains. The best-fit scenarios require a small iDM fraction ($f_ ext{idm}\sim1$–$3\%$) and a modest DR contribution ($\Delta N_ ext{eff}\sim0.7$–$0.9$), yielding $H_0\approx72$ km/s/Mpc in Planck-consistent fits, but ACT DR6 reduces this improvement, underscoring the strong leverage of small-scale CMB data for these models.

Abstract

Models in which a subcomponent of dark matter interacts with dark radiation have been proposed as a solution to the Hubble tension. In this framework, the interacting subcomponent of dark matter is in thermal equilibrium with the dark radiation in the early universe, but decouples from it around the time of matter-radiation equality. We study this general class of models and evaluate the quality of fit to recent cosmological data on the cosmic microwave background (from Planck 2018 and ACT DR6), baryon acoustic oscillations, large-scale structure, supernovae type Ia, and Cepheid variables. We focus on three benchmark scenarios that differ in the rate at which the dark matter decouples from the dark radiation, resulting in different patterns of dark acoustic oscillations. Fitting without ACT DR6 data, we find that all three scenarios significantly reduce the Hubble tension relative to $Λ$CDM, with an exponentially fast decoupling being the most preferred. The tension is reduced to less than $2 \, σ$ in fits that don't include the SH0ES collaboration results as part of the data and to less than $1 \, σ$ when these are included. When ACT DR6 data is included, the fit is significantly worsened. We find that the largest $H_0$ value at the $95 \%$ confidence region is $70.1$ km/s/Mpc without the SH0ES data, leading to only a mild reduction in the tension. This increases to $72.5$ km/s/Mpc, corresponding to a reduction in the tension to less than $3 \, σ$, if the SH0ES results are included in the fit.

Figures (19)

• Figure 1: Feynman diagrams for different dark sector interactions considered in this work. $\chi$ denotes the interacting dark matter (iDM), while $\xi$, $A'$, and $\psi$ represent the dark radiation (DR) components corresponding to $n=4$, $n=2$, and $n=0$ cases, respectively. Left: Four-fermion interaction ($n=4$). Middle: Compton-like scattering ($n=2$). Right: Coulomb-like scattering ($n=0$).
• Figure 2: Ratio of the MPS of the $\text{gen-iDM}$ models to that of purely self-interacting dark radiation (SIDR) Brust:2017nmvBlinov:2020hmc, for different choices of $f_\mathrm{idm}$ (left panel) and $\log_{10}\left( z_\mathrm{dec} \right)$ (right panel). We have fixed $\Delta N_\mathrm{eff}\xspace = 0.1$ throughout. The $\theta_s$, $\omega_b$, $A_s$, $n_s$, and $\tau_{\rm reio}$ parameters have been fixed to their mean values in the Planck $\Lambda\mathrm{CDM}$ fit to TT+TE+EE+lowE+lensing+BAO data Planck:2018vyg. In order to keep the time of matter-radiation equality the same as in Ref. Planck:2018vyg in the presence of additional DR ($z_\mathrm{eq} = 3387$), we choose $\omega_\mathrm{dm} = 0.121$. Left: varying $f_\mathrm{idm}$ from $2\%$ to $10\%$ in $4\%$ increments, while fixing $\log_{10}\left( z_\mathrm{dec} \right) = 3.5$. Right: varying $\log_{10}\left( z_\mathrm{dec} \right)$ from $2.5$ to $3.5$ in incremenets of $0.5$, while fixing $f_\mathrm{idm} = 4\%$.
• Figure 3: Residuals of the CMB $C_\ell^{TT}$ (left) and $C_\ell^{EE}$ (right) for $\text{gen-iDM}$ models compared to those of SIDR, for different choices of $f_\mathrm{idm}$ (top) and $\log_{10}\left( z_\mathrm{dec} \right)$ (bottom). All other parameters are fixed as in Fig. \ref{['fig:rainbow_pk']}.
• Figure 4: $C_\ell^{TT}$ (top) and $C_\ell^{EE}$ (bottom) residuals of the $\text{gen-iDM}$ models compared to $\Lambda\mathrm{CDM}$, using the best fit point of each model to the $\mathcal{P}$ (red), $\mathcal{PH}$ (green), and $\mathcal{PHF}$ (blue) datasets.
• Figure 5: Ratios of the linear MPS in the $\text{gen-iDM}$ models to that in the $\Lambda\mathrm{CDM}$ model, for the best fit point of each model to the $\mathcal{P}$ (upper left), $\mathcal{PH}$ (upper right), and $\mathcal{PHF}$ (lower) datasets. In all curves one can clearly see the effect of the dark acoustic oscillations. In some of the figures, one can also observe a little interference between the dark acoustic oscillations and BAO.