Supergravity Model of Inflation and Explaining IceCube HESE Data via PeV Dark Matter Decay

Abstract

We construct an unified model of inflation and PeV dark matter with an appropriate choice of no-scale Kähler 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 $(γ, β)$ and coupling $ζ$ value in producing the correct amplitude of CMB power spectrum. However the value of parameter $\tan(β)=1.8$, 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.