Flavour specific neutrino self-interaction: $H_0$ tension and IceCube
  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 interaction considered for solving the $H_0$ tension, which
is ruled out from particle physics experiments, we consider flavour specific
neutrino interactions. 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 BAO, HST and Planck data. However, the required amount of
self-interaction between tau neutrinos ($\nu_\tau$) in inverted hierarchy for
explaining IceCube dips is consistent with the moderate self-interaction region
of cosmological bounds at 1-$\sigma$ level. For the case of other interactions
and hierarchies, the IceCube preferred amount of self-interaction is consistent
with moderate self-interaction region of cosmological bounds at 2-$\sigma$
level only.
