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.