On the dark radiation role in the Hubble constant tension

Dark radiation, parameterized in terms of $N_{\mathrm{e}\mathrm{f}\mathrm{f}}$, has been considered many times in the literature as a possible remedy in alleviating the Hubble constant ($H_0$) tension. We review here the effect of such an extra dark radiation component in the different cosmological observables, focusing mostly on $H_0$. While a larger value of $N_{\mathrm{e}\mathrm{f}\mathrm{f}}$ automatically implies a larger value of the Hubble constant, and one would naively expect that such a simple scenario provides a decent solution, more elaborated models are required. Light sterile neutrinos or neutrino asymmetries are among the first-order corrections to the most economical (tree-level) massless dark radiation scenario. However, they are not fully satisfactory in solving the $H_0$ issue. We devote here special attention to second-order corrections: some interacting scenarios, such as those with new dark radiation degrees of freedom that exhibit a non-free streaming nature are highly satisfactory alternative cosmologies where to solve the Hubble constant tension. Models with self-interacting sterile neutrinos and/or majorons, both well-motivated beyond the Standard Model particles, will be discussed along our assessment.