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Several interesting Dark Matter (DM) models invoke a dark sector leading totwo types of relic particles, possibly interacting with each other:non-relativistic DM, and relativistic Dark Radiation (DR). These models haveinteresting consequences for cosmological observables, and could in principlesolve problems like the small-scale cold DM crisis, Hubble tension, and/or low$\sigma_8$ value. Their cosmological behaviour is captured by the ETHOSparametrisation, which includes a DR-DM scattering rate scaling like apower-law of the temperature, $T^n$. Scenarios with $n=0$, $2$, or $4$ caneasily be realised in concrete dark sector set-ups. Here we update constraintson these three scenarios using recent CMB, BAO, and high-resolutionLyman-$\alpha$ data. We introduce a new Lyman-$\alpha$ likelihood that isapplicable to a wide range of cosmological models with a suppression of thematter power spectrum on small scales. For $n=2$ and $4$, we find thatLyman-$\alpha$ data strengthen the CMB+BAO bounds on the DM-DR interaction rateby many orders of magnitude. However, models offering a possible solution tothe missing satellite problem are still compatible with our new bounds. For$n=0$, high-resolution Lyman-$\alpha$ data bring no stronger constraints on theinteraction rate than CMB+BAO data, except for extremely small values of the DRdensity. Using CMB+BAO data and a theory-motivated prior on the minimal densityof DR, we find that the $n=0$ model can reduce the Hubble tension from$4.1\sigma$ to $2.7\sigma$, while simultaneously accommodating smaller valuesof the $\sigma_8$ and $S_8$ parameters hinted by cosmic shear data.

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