Primordial neutrinos fade to gray: constraints from cosmological observables

We investigate the effect of potentially large distortions of the relic neutrino spectra on cosmological observables. To that end, we consider a phenomenological model of "gray" spectral distributions, described by a single parameter, which generalizes the traditional $y$-distortions to possibly large negative values. Implementing these distortions in the primordial nucleosynthesis code PRIMAT, we can constrain the distortion parameter along with the presence of extra radiation, exploiting the complementarity of big bang nucleosynthesis and cosmic microwave background measurements to disentangle gravitational and non-thermal effects. These constraints rule out a distortion where more than $\sim 1/2$ of the neutrinos' energy density is replaced by dark radiation. Nonetheless, we find that large distortions, accompanied with extra radiation, are allowed-and even slightly preferred in some cases-by current cosmological observations. As this scenario would require substantial modifications to the physics of neutrino decoupling in the early Universe, these observational constraints call for a renewed attention on the possibility of large deviations from the standard cosmological model in the neutrino sector.