  We consider the effects of active-sterile secret neutrino interactions,
mediated by a new pseudoscalar particle, on high- and ultra high-energy
neutrino fluxes. In particular, we focus on the case of 3 active and 1 sterile
neutrino coupled by a flavor dependent interaction, extending the case of 1
active and 1 sterile neutrino we have recently examined. We find that,
depending on the kind of interaction of sterile neutrino with the active
sector, new regions of the parameter space for secret interactions are now
allowed leading to interesting phenomenological implications on two benchmark
fluxes we consider, namely an astrophysical power law flux, in the range below
100 PeV, and a cosmogenic flux, in the Ultrahigh energy range. First of all,
the final active fluxes can present a measurable depletion observable in future
experiments. Especially, in the case of only tau neutrino interacting, we find
that the effects on the astrophysical power law flux can be so large to be
already probed by the IceCube experiment. Moreover, we find intriguing features
in the energy dependence of the flavor ratio.
