# Is the $H_0$ tension suggesting a 4th neutrino's generation?

## TL;DR

This study investigates whether the tension in the Hubble constant measurements suggests the existence of a fourth neutrino, using cosmological data and models, and finds evidence favoring an extra relativistic species.

## Contribution

The paper performs a joint analysis of multiple cosmological distance measurements to test the existence of a fourth neutrino species, finding support for $N_{eff}
eq 3$.

## Key findings

- Best-fit $N_{eff} \\approx 4$ in both models.
- Standard $N_{eff} \\approx 3$ is ruled out at about 3 sigma.
- Chaplygin gas parameter slightly negative, $\\alpha \\approx -0.04$.

## Abstract

Flavour oscillations experiments are suggesting the existence of a sterile, $4$th neutrino's 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 $N_{eff} \approx 3$ for the effective number of relativistic species. On the other hand, the Planck best-fit for the Hubble-Lema\^itre 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 CMB acoustic scale measured by Planck, the BAO scale model-independently determined by Verde {\it et al.}, and luminosity distances measured with JLA and Pantheon SNe Ia surveys. Two Gaussian priors were imposed to the analysis, the local expansion rate measured by Riess {\it et al.}, and the baryon density parameter fixed from primordial nucleosynthesis by Cooke {\it et al.}. For the sake of generality, two different models are used in the tests, the standard $\Lambda$CDM model and a generalised Chaplygin gas. The best-fit gives $N_{eff} \approx 4$ in both models, with a Chaplygin gas parameter slightly negative, $\alpha \approx -0.04$. The standard value $N_{eff} \approx 3$ is ruled out with $\approx 3\sigma$.