Constraining Dark Matter -- Dark Radiation interactions with CMB, BAO, and Lyman-$α$

TL;DR

This work investigates DM-DR interacting models within the ETHOS framework for $n\in\{0,2,4\}$ using Planck+BAO data augmented by a new high-resolution Lyman-$\alpha$ likelihood that maps small-scale power suppression to a three-parameter transfer function $(\alpha,\beta,\gamma)$. By implementing the ETHOS DM-DR physics in CLASS and employing a wide grid of hydrodynamical simulations calibrated to HIRES/MIKE data, the authors derive robust constraints on the DR density and interaction strength, revealing that Lyman-$\alpha$ data dramatically tighten bounds for $n=2$ and $n=4$, while $n=0$ remains more model- and prior-dependent. The main results show upper bounds on the DR density $\Delta N_{eff}$ around $0.23$–$0.29$ and on the interaction combination $a_{dark}\xi^4$ at the level of $\mathcal{O}(10)$–$\mathcal{O}(30)\,\mathrm{Mpc}^{-1}$, with Planck+BAO+Lyman-$\alpha$ not strongly preferring a departure from $\Lambda$CDM. In the $n=0$ case, a particle-physics-motivated prior can partially alleviate the $H_0$ tension and reduce $\sigma_8$ toward observational hints, but these results are sensitive to prior choices and the modelling limits of the Lyman-$\alpha$ method. Overall, DM-DR interactions remain viable under current data, and the Lyman-$\alpha$ likelihood developed here provides a powerful, generalizable tool for testing small-scale suppression scenarios in the dark sector.

Abstract

Several interesting Dark Matter (DM) models invoke a dark sector leading to two types of relic particles, possibly interacting with each other: non-relativistic DM, and relativistic Dark Radiation (DR). These models have interesting consequences for cosmological observables, and could in principle solve problems like the small-scale cold DM crisis, Hubble tension, and/or low $σ_8$ value. Their cosmological behaviour is captured by the ETHOS parametrisation, which includes a DR-DM scattering rate scaling like a power-law of the temperature, $T^n$. Scenarios with $n=0$, $2$, or $4$ can easily be realised in concrete dark sector set-ups. Here we update constraints on these three scenarios using recent CMB, BAO, and high-resolution Lyman-$α$ data. We introduce a new Lyman-$α$ likelihood that is applicable to a wide range of cosmological models with a suppression of the matter power spectrum on small scales. For $n=2$ and $4$, we find that Lyman-$α$ data strengthen the CMB+BAO bounds on the DM-DR interaction rate by many orders of magnitude. However, models offering a possible solution to the missing satellite problem are still compatible with our new bounds. For $n=0$, high-resolution Lyman-$α$ data bring no stronger constraints on the interaction rate than CMB+BAO data, except for extremely small values of the DR density. Using CMB+BAO data and a theory-motivated prior on the minimal density of DR, we find that the $n=0$ model can reduce the Hubble tension from $4.1σ$ to $2.7σ$, while simultaneously accommodating smaller values of the $σ_8$ and $S_8$ parameters hinted by cosmic shear data.

Figures (6)

• Figure 1: (Left) Linear transfer functions $T(k)^2=P(k)/P(k)^{\Lambda \mathrm{CDM}}$ at $z=0$, for $n=4$ (top row), $n=2$ (second row), $n=0$ (bottom row). The different colours correspond to different values of the amount of dark radiation $\xi$ and of the strength of the interaction $a_\mathrm{dark}$. Solid lines depict the true $T(k)^2$, while dashed lines of the same colour show the corresponding $\{\alpha, \beta, \gamma \}$-fit. (Right) Relative deviation of the $\{\alpha, \beta, \gamma \}$-fit from the true $T(k)^2$ (solid lines) for the same models (colours) as in the left panel. The vertical lines show $k_{1/2}$ (dot-dashed lines) and $k_\mathrm{fit}$ (dashed lines - for $n=0$, $k_\mathrm{fit}=k_\mathrm{max}$). The grey shaded region approximately represents the $k$ range probed by Lyman-$\alpha$ data.
• Figure 2: Ratio between the non-linear matter power spectra (left panel) and the corresponding ratio of 1D flux power spectrum (right panel) at $z=5$. The spectra are obtained from simulations with the linear input given either by the true $T(k)$ (solid lines) or by the fit $T(k,\alpha,\beta,\gamma)$. The theoretical model is $n=4$ and it has $\xi=0.5$ and $a_\mathrm{dark}=3\times10^5\,\mathrm{Mpc}^{-1}$. The grey shaded region defines the $k$ range of MIKE/HIRES data.
• Figure 3: (Left) Two-dimensional posterior distributions for all main parameters for the $n = 4$ case, with Planck + BAO (red), Planck + BAO + Lyman-$\alpha$ Data (dark blue), and the Lyman-$\alpha$ Prior check run explained in the text (light blue), when running with a flat prior on $\xi$ and logarithmic prior on $a_\mathrm{dark}$. The smoothing has deliberately been turned off to show the sharp boundaries of the preferred regions more clearly. (Right) Posterior distributions when using linear priors on $\Delta N_\mathrm{eff}$ and $a_\mathrm{dark}\xi^4$.
• Figure 4: (Left) Two-dimensional posterior distributions for all main parameters for the $n = 2$ case, with Planck + BAO (red), Planck + BAO + Lyman-$\alpha$ Data (dark blue), and the Lyman-$\alpha$ Prior check run explained in the text (light blue), when running with a flat prior on $\xi$ and logarithmic prior on $a_\mathrm{dark}$. The smoothing has deliberately been turned off to show the sharp boundaries of the preferred regions more clearly. (Right) Posterior distributions when using linear priors on $\Delta N_\mathrm{eff}$ and $10^2 a_\mathrm{dark}\xi^4$.
• Figure 5: (Left) Two-dimensional posterior distributions for all main parameters for the $n = 0$ case, with Planck + BAO (red), Planck + BAO + Lyman-$\alpha$ Data (dark blue), and the Lyman-$\alpha$ Prior check run explained in the text (light blue), when running with a flat prior on $\xi$ and logarithmic prior on $a_\mathrm{dark}$. The smoothing has deliberately been turned off to show the sharp boundaries of the preferred regions more clearly. (Right) Posterior distributions when using linear priors on $\Delta N_\mathrm{fluid}$ and $10^4 a_\mathrm{dark}\xi^4$.