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The number of relativistic species, $N_{\rm eff}$, has been preciselycalculated in the standard model, and would be measured to the percent level byCMB-S4 in future. Neutral-current non-standard interactions would affectneutrino decoupling in the early Universe, thus modifying $N_{\rm eff}$. Weparameterize those operators up to dimension-7 in the effective field theoryframework, and then provide a complete, generic and analytical dictionary forthe collision term integrals. From precision measurements of $N_{\rm eff}$, themost stringent constraint is obtained for the dimension-6 vector-typeneutrino-electron operator, whose scale is constrained to be above about 195(331) GeV from Planck (CMB-S4). We find our results complementary to otherexperiments like neutrino coherent scattering, neutrino oscillation, collider,and neutrino deep inelastic scattering experiments.

Neutrino non-standard interactions meet precision measurements of $N_{\rm eff}$