Title: Dark Radiation with Baryon Acoustic Oscillations from DESI 2024 and the $H_0$ tension

Abstract: We investigate the presence of extra relativistic degrees of freedom in the early Universe, contributing to the effective number of neutrinos $N_\text{eff}$, as $\Delta N_\text{eff}\equiv N_\text{eff}-3.044\geq 0$, in light of the recent measurements of Baryon Acoustic Oscillations (BAO) by the DESI collaboration. We analyze one-parameter extensions of the $\Lambda$CDM model where dark radiation (DR) is free streaming or behaves as a perfect fluid, due to self-interactions. We report a significant relaxation of upper bounds on $\Delta N_\text{eff}$, with respect to previous BAO data from SDSS+6dFGS, when additionally employing Planck data (and supernovae data from Pantheon+), setting $\Delta N_\text{eff}\leq 0.39$ ($95\%$ C.L.) for free streaming DR, and a very mild preference for fluid DR, $\Delta N_\text{eff} = 0.221^{+0.088}_{-0.18}$ ($\leq 0.46$, $95\%$ C.L.). Applying constraints from primordial element abundances leads to slightly tighter constraints on $\Delta N_\text{eff}$, but they are avoided if DR is produced after Big Bang Nucleosynthesis (BBN). For fluid DR we estimate the tension with the SH$_0$ES determination of $H_0$ to be around $(2.3-2.8)\sigma$ level, and for free-streaming DR the tension is below $3\sigma$ if production occurs after BBN. This lesser degree of tension motivates a combination with SH$_0$ES in these cases, resulting in a $4.4\sigma-5\sigma$ evidence for dark radiation with $\Delta N_\text{eff}\simeq 0.6$ and large improvements in $\chi^2$ over $\Lambda$CDM, $-18\lesssim \Delta \chi^2\lesssim -25$.