Multi-component Dark Matter and leptogenesis with double seesaw in an extended left-right symmetric theory

Left-Right Symmetric theory has proved to be one of the most successful models in explaining the origin of neutrino mass and mixings, and the phenomenological origin of neutrinoless double beta decay, lepton flavor violation as well as leptogenesis within its regime. In the current work, left-right symmetric model has been extended with a sterile neutrino per generation, which acts as a dark matter candidate within the model. The model has been realized using $A_4$ modular symmetry and the primary focus of the work rests on investigating the impact of assigning different modular weights to the particle content of the model and hence study its effects on the results pertaining to relic abundance of dark matter and also leptogenesis within its framework.