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Of the many proposed extensions to the $\Lambda$CDM paradigm, a model inwhich neutrinos self-interact until close to the epoch of matter-radiationequality has been shown to provide a good fit to current cosmic microwavebackground (CMB) data, while at the same time alleviating tensions withlate-time measurements of the expansion rate and matter fluctuation amplitude.Interestingly, CMB fits to this model either pick out a specific large value ofthe neutrino interaction strength, or are consistent with the extremely weakneutrino interaction found in $\Lambda$CDM, resulting in a bimodal posteriordistribution for the neutrino self-interaction cross section. In this paper, weexplore why current cosmological data select this particular large neutrinoself-interaction strength, and by consequence, disfavor intermediate values ofthe self-interaction cross section. We show how it is the $\ell \gtrsim 1000$CMB temperature anisotropies, most recently measured by the Planck satellite,that produce this bimodality. We also establish that smaller scale temperaturedata, and improved polarization data measuring the temperature-polarizationcross-correlation, will best constrain the neutrino self-interaction strength.We forecast that the upcoming Simons Observatory should be capable ofdistinguishing between the models.

$\Lambda$CDM or self-interacting neutrinos? - how CMB data can tell the two models apart