Is the H0 tension suggesting a fourth neutrino generation?

Flavor oscillations experiments are suggesting the existence of a sterile, fourth neutrino generation with a mass of an eV order. This would mean an additional relativistic degree of freedom in the cosmic inventory, in contradiction with recent results from the Planck satellite, that have confirmed the standard value N-eff approximate to 3 for the effective number of relativistic species. On the other hand, the Planck best-fit for the Hubble-Lemaitre parameter is in tension with the local value determined with the Hubble Space Telescope, and adjusting N-eff is a possible way to overcome such a tension. In this paper we perform a joint analysis of three complementary cosmological distance rulers, namely the cosmic microwave backgroune acoustic scale measured by Planck, the baryonic acoustic oscillation scale model-independently determined by Verde et al., and luminosity distances measured with Joint Light-curves Analysis and Pantheon SNe Ia surveys. Two Gaussian priors were imposed to the analysis, the local expansion rate measured by Riess et al. and the baryon density parameter fixed from primordial nucleosynthesis by Cooke et al.. For the sake of generality and robustness, two different models are used in the tests, the standard Lambda CDM model and a generalized Chaplygin gas. The best-fit gives N-eff approximate to 4 in both models, with a Chaplygin gas parameter slightly negative, alpha approximate to -0.04. The standard value N-eff approximate to 3 is ruled out with approximate to 3 sigma.