keV Sterile Neutrino as Dark Matter in Doublet Left-Right Symmetric Model with <i>A</i> 4 Modular Symmetry

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