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Dark radiation (DR) appears as a new physics candidate in various scenariosbeyond the Standard Model. While it is often assumed that perturbations in DRare adiabatic, they can easily have an isocurvature component if more than onefield was present during inflation, and whose decay products did not allthermalize with each other. By implementing the appropriate isocurvatureinitial conditions (IC), we derive the constraints on both uncorrelated andcorrelated DR density isocurvature perturbations from the full Planck 2018 dataalone, and also in combination with other cosmological data sets. Our study onfree-streaming DR (FDR) updates and generalizes the existing bound on neutrinodensity isocurvature perturbations by including a varying number ofrelativistic degrees of freedom, and for coupled DR (CDR) isocurvature, wederive the first bound. We also show that for CDR qualitatively new physicaleffects arise compared to FDR. One such effect is that for isocurvature IC, FDRgives rise to larger CMB anisotropies compared to CDR -- contrary to theadiabatic case. More generally, we find that a blue-tilt of DR isocurvaturespectrum is preferred. This gives rise to a larger value of the Hubble constant$H_0$ compared to the standard $\Lambda$CDM+$\Delta N_{\rm eff}$ cosmology withadiabatic spectra and relaxes the $H_0$ tension.

Free-streaming and Coupled Dark Radiation Isocurvature Perturbations: Constraints and Application to the Hubble Tension