We perform a comprehensive study of cosmological constraints on nonstandard neutrino self-interactions using cosmic microwave background and baryon acoustic oscillation data. We consider different scenarios for neutrino self-interactions distinguished by the fraction of neutrino states allowed to participate in self-interactions and how the relativistic energy density, $N_{\mathrm{eff}}$, is allowed to vary. Specifically, we study cases in which all neutrino states self-interact and $N_{\mathrm{eff}}$ varies; two species free-stream, which we show alleviates tension with laboratory constraints, while the energy in the additional interacting states varies; and a variable fraction of neutrinos self-interact with either the total $N_{\mathrm{eff}}$ fixed to the Standard Model value or allowed to vary. In no case do we find compelling evidence for new neutrino interactions or nonstandard values of $N_{\mathrm{eff}}$. In several cases, we find additional modes with neutrino decoupling occurring at lower redshifts $z_{\mathrm{dec}}\sim {10}^{3–4}$. We do a careful analysis to examine whether new neutrino self-interactions solve or alleviate the so-called $H_0$ tension and find that, when all Planck 2018 CMB temperature and polarization data are included, none of these examples eases the tension more than allowing a variable $N_{\mathrm{eff}}$ comprised of free-streaming particles. Although we focus on neutrino interactions, these constraints are applicable to any light relic particle.

• Received 18 February 2021
• Accepted 1 July 2021

DOI:https://doi.org/10.1103/PhysRevD.104.063523