$keV$ sterile neutrino as dark matter in doublet left-right symmetric model with $A_{4}$ modular symmetry

Abstract

Left-Right Symmetric Model(LRSM) in this work is extended with a sterile fermion per generation, the lightest of the same is considered to be a suitable dark matter candidate for the study and analysis of the associated properties. The model has been realized using $A_{4}$ modular symmetry, the advantage being the non-requirement of the use of extra fields, hence keeping the model minimal. Because of the extension of LRSM with the sterile fermion, the neutrino mass in this work will be generated by the double seesaw mechanism as described thoroughly within the manuscript. And for phenomenological studies, we have considered neutrinoless double beta decay the details of which have been discussed thoroughly within the work.