Global view of neutrino interactions in cosmology: The freestreaming window as seen by Planck

Neutrinos are expected to freestream (i.e. not interact with anything) since they decouple in the early Universe at a temperature $T\sim 2\mathrm{M}\mathrm{e}\mathrm{V}$. However, there are many relevant particle physics scenarios that can make neutrinos interact at $T<2\mathrm{M}\mathrm{e}\mathrm{V}$. In this work, we take a global perspective and aim to identify the temperature range in which neutrinos can interact given current cosmological observations. We consider a generic set of rates parametrizing neutrino interactions and by performing a full Planck cosmic microwave background (CMB) analysis we find that neutrinos cannot interact significantly for redshifts $2000\lesssim z\lesssim {10}^5$, which we refer to as the freestreaming window. We also derive a redshift dependent upper bound on a suitably defined interaction rate ${\mathrm{\Gamma }}_{\text{nfs}}(z)$, finding ${\mathrm{\Gamma }}_{\text{nfs}}(z)/H(z)\lesssim 1-10$ within the freestreaming window. We show that these results are largely model independent under some broad assumptions, and contextualize them in terms of neutrino decays, neutrino self-interactions, neutrino annihilations, and majoron models. We provide examples of how to use our model independent approach to obtain bounds in specific scenarios, and demonstrate agreement with existing results. We also investigate the reach of upcoming cosmological data finding that CMB Stage-IV experiments can improve the bound on ${\mathrm{\Gamma }}_{\text{nfs}}(z)/H(z)$ by up to a factor $10$. Moreover, we comment on large-scale structure observations, finding that the ongoing DESI survey has the potential to probe uncharted regions of parameter space of interacting neutrinos. Finally, we point out a peculiar scenario that has so far not been considered, and for which relatively large interactions around recombination are still allowed by Planck data due to some degeneracy with $n_s$, $A_s$ and $H_0$. This scenario can be fully tested with CMB-S4.