Neutrino non-standard interactions meet precision measurements of Neff

The number of relativistic species, Neff, has been precisely calculated in the standard model, and would be measured to the percent level by CMB-S4 in future. Neutral-current non-standard interactions would affect neutrino decoupling in the early Universe, thus modifying Neff. We parameterize those operators up to dimension-7 in the effective field theory framework, and then provide a complete, generic and analytical dictionary for the collision term integrals. From precision measurements of Neff, the most stringent constraint is obtained for the dimension-6 vector-type neutrino-electron operator, whose scale is constrained to be above about 195 (331) GeV from Planck (CMB-S4). We find our results complementary to other experiments like neutrino coherent scattering, neutrino oscillation, collider, and neutrino deep inelastic scattering experiments.