Supergravity Model of Inflation and Explaining IceCube HESE Data via PeV
  Dark Matter Decay
  We construct an unified model of inflation and PeV dark matter with an
appropriate choice of no-scale K\"ahler potential, superpotential and gauge
kinetic function in terms of MSSM fields and hidden sector Polonyi field. The
model is consistent with the CMB observations and can explain the PeV neutrino
flux observed at IceCube HESE. A Starobinsky like Higgs-sneutrino plateau
inflation is obtained from the $D$-term SUGRA potential while $F$-term being
subdominant during inflation. To get PeV dark matter, SUSY breaking at PeV
scale is achieved through Polonyi field. This sets the scale for soft SUSY
breaking parameters $m_0, m_{1/2}, A_0 $ at the GUT scale in terms of the
parameters of the model. The low energy particles spectrum is obtained by
running the RGEs. We show that the $\sim$125 GeV higgs and the gauge coupling
unification can be obtained in this model. The $6$ PeV bino-type dark matter is
a subdominant fraction ($\sim 11\%$) of the relic density and its decay gives
the PeV scale neutrino flux observed at IceCube by appropriately choosing the
couplings of the $R$-parity violating operators. Also we find that there is a
degeneracy in scalar field parameters $(\gamma, \beta)$ and coupling $\zeta$
value in producing the correct amplitude of CMB power spectrum. However the
value of parameter $\tan(\beta)=1.8$, which is tightly fixed from the
requirement of PeV scale SUSY breaking, removes the degeneracy in the values of
the scalar field parameters to provide a unique solution for inflation. In this
way it brings the explanation for dark matter, PeV neutrinos and inflation
within the same framework.
