Multi-component Fermionic Dark Matter and IceCube PeV scale Neutrinos in
  Left-Right Model with Gauge Unification
  We consider a simple extension of the minimal left-right symmetric model
(LRSM) in order to explain the PeV neutrino events seen at the IceCube
experiment from a heavy decaying dark matter. The dark matter sector is
composed of two fermions: one at PeV scale and the other at TeV scale such that
the heavier one can decay into the lighter one and two neutrinos. The gauge
annihilation cross sections of PeV dark matter are not large enough to generate
its relic abundance within the observed limit. We include a pair of real scalar
triplets $\Omega_{L,R}$ which can bring the thermally overproduced PeV dark
matter abundance into the observed range through late time decay and consequent
entropy release thereby providing a consistent way to obtain the correct relic
abundance without violating the unitarity bound on dark matter mass. Another
scalar field, a bitriplet under left-right gauge group is added to assist the
heavier dark matter decay. The presence of an approximate global $U(1)_X$
symmetry can naturally explain the origin of tiny couplings required for
long-lived nature of these decaying particles. We also show, how such an
extended LRSM can be incorporated within a non-supersymmetric $SO(10)$ model
where the gauge coupling unification at a very high scale naturally accommodate
a PeV scale intermediate symmetry, required to explain the PeV events at
IceCube.
