Leptogenesis as an origin of hot dark matter and baryon asymmetry in the E6 inspired SUSY models

We explore leptogenesis within the $E_6$ inspired $U\left(1\right)$ extension of the MSSM in which exact custodial symmetry forbids tree-level flavour-changing transitions and the most dangerous baryon and lepton number violating operators. This supersymmetric (SUSY) model involves extra exotic matter beyond the MSSM. In the simplest phenomenologically viable scenarios the lightest exotic fermions are neutral and stable. These states should be substantially lighter than $1\text{eV}$ forming hot dark matter in the Universe. The low-energy effective Lagrangian of the SUSY model under consideration possesses an approximate global $U{\left(1\right)}_E$ symmetry associated with the exotic states. The $U{\left(1\right)}_E$ symmetry is explicitly broken because of the interactions between the right-handed neutrino superfields and exotic matter supermultiplets. As a consequence the decays of the lightest right-handed neutrino/sneutrino give rise to both $U{\left(1\right)}_E$ and $U{\left(1\right)}_{B-L}$ asymmetries. When all right-handed neutrino/sneutrino are relatively light $\sim {10}^6\text{–}{10}^7\text{GeV}$ the appropriate amount of the baryon asymmetry can be induced via these decays if the Yukawa couplings of the lightest right-handed neutrino superfields to the exotic matter supermultiplets vary between $\sim {10}^{-4}\text{–}{10}^{-3}$.