Bound on thermal y distortion of the cosmic neutrino background

We consider the possibility that the cosmic neutrino background might have a nonthermal spectrum, and investigate its effect on cosmological parameters relative to standard Λ-cold dark matter (ΛCDM) cosmology. As a specific model, we consider a thermal y-distortion, which alters the distribution function of the neutrino background by depleting the population of low-energy neutrinos and enhancing the high-energy tail. We constrain the thermal y-parameter of the cosmic neutrino background using cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) measurements, and place a 95%-confidence upper bound of y≤0.043. The y-parameter increases the number of effective relativistic degrees of freedom, reducing the sound horizon radius and increasing the best-fit value for the Hubble constant H0. We obtain an upper bound on the Hubble constant of H0=71.12 km/s/Mpc at 95% confidence, substantially reducing the tension between CMB/BAO constraints and direct measurement of the expansion rate from type-Ia supernovae. Including a spectral distortion also allows for a higher value of the spectral index of scalar fluctuations, with a best-fit of nS=0.9720±0.0063, and a 95%-confidence upper bound of nS≤0.9842.