Abstract
Self interaction in the active neutrinos is studied in the literature to
alleviate the $H_0$ tension. Similar self-interaction can also explain the
observed dips in the flux of the neutrinos, coming from the distant
astro-physical sources, in IceCube detectors. In contrast to the flavour
universal neutrino interactions considered for solving the $H_0$ tension, which
is ruled out from particle physics experiments, we consider flavour specific
neutrino interactions in CMB and IceCube data. We show that the values of
self-interaction coupling constant and mediator mass required for explaining
the IceCube dips are inconsistent with the strong neutrino self-interactions
preferred by the combination of the HST and Planck data. However, the smaller
amount of self-interaction between $\nu_\tau$ can explain the resonant
absorption features in IceCube data and help in solving the $H_0$ tension.
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