Flavor-universal neutrino self-interaction has been shown to ease the tension between the values of the Hubble constant measured from early and late Universe data. We introduce a self-interaction structure that is flavor-specific in the three active neutrino framework. This is motivated by the stringent constraints on new secret interactions among electron and muon neutrinos from several laboratory experiments. Our study indicates the presence of a strongly interaction mode which implies a late-decoupling of the neutrinos just prior to matter radiation equality. Using the degeneracy of the coupling strength with other cosmological parameters, we explain the origin of this new mode as a result of better fit to certain features in the CMB data. We find that if only one or two of the three active neutrino flavors are interacting, then the statistical significance of the strongly-interacting neutrino mode increases substantially relative to the flavor-universal scenario. However, the central value of the coupling strength for this interaction mode does not change by any appreciable amount in the flavor-specific cases. We also briefly analyze a scenario with more than three neutrino species of which only one is self-interacting. In none of the cases, we find a large enough Hubble constant that could resolve the so-called Hubble tension.
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