Extending the MSSM with singlet Higgs and right handed neutrino for the self-interacting dark matter

In order to meet the requirement of BBN, the right handed neutrino is added to the singlet Higgs sector in the GNMSSM. The spectrum and Feynman rules are calculated. the dark matter phenomenology is also studied. In case of $\l\sim 0$, the singlet sector can give perfect explanation of relic abundance of dark matter and small cosmological structure simulations. The BBN constraints on the light mediator can be easily solved by decaying to the right handed neutrino. When the ${\text{l}}_N$ is at the order of $\mathcal{O}(0.1)$, the mass of the mediator can be constrained to several MeV