  The short-baseline neutrino oscillation experiments, the excess of radiation
from the measurement of the cosmic microwave background radiation, the
necessity of the nonbaryonic dark matter candidate and the depletion of the
neutrino flux in IceCube all seem to hint at new physics beyond the standard
model. An economical way to address these issues is to invoke the existence of
sterile neutrinos. We present simple extensions of the standard model with
additional three sterile neutrinos and discuss the corresponding PMNS like
neutrino flavor mixing matrix. The noteworthy features of the sterile neutrino
scenario advocated here is that the lightest one is almost degenerate with one
of the active neutrinos, the second sterile has mass of order eV and the
heaviest one is in the keV range. In the present scenario, the short baseline
anomaly is explained through $\Delta m^2\sim 1\, {\rm eV^2}$, the depletion of
muon neutrino flux in IceCube is explained through $\Delta m^2\sim 4.0\times
10^{-16}\, {\rm eV^2}$ and the dark matter problem is addressed through $\Delta
m^2\sim 1\, {\rm keV^2}$. Our proposed mixing matrix is also compatible with
the observed neutrino oscillation data. We show that the high energy muon and
the tau neutrino fluxes from Gamma Ray Bursts can be depleted in IceCube by as
much as 38% and 43% respectively. These substantial depletion in both muon and
tau neutrino fluxes is due to their small but sizable mixing with the sterile
neutrinos.
