Leptogenesis and dark matter in minimal inverse seesaw using $A_4$ modular symmetry

In this paper we have studied neutrino masses and mixings by adding a scalar triplet $\eta$ to the particle content of minimal inverse seesaw. We have realised this extension of minimal inverse seesaw by implementing an isomorphic modular group $\Gamma(3)$ and a non-abelian discrete symmetry group $A_4$. We have also used $Z_3$ symmetry group to restrain certain interaction terms in the lagrangian of the model. We have studied baryon asymmetry of the universe, neutrinoless double-beta decay and dark matter in our work. In order to check the consistency of our model with various experimental constraints, we have therefore calculated effective mass, relic density and baryogenesis via leptogenesis. Interestingly, we have found our model quite compatible with the experimental bounds and is also successful in producing the neutrino masses and mixings in the 3$\sigma$ range.