A modular $A_4$ symmetric Scotogenic model for Neutrino mass and Dark Matter

Modular symmetries have been impeccable in neutrino and quark sectors. This motivated us, therefore, to propose a variant of scotogenic model based on modular $A_4$ symmetry to realize the neutrino mass generation at one-loop level through radiative mechanism. Alongside, the lepton flavour violating process $\mu \to e \gamma$ and the muon $g-2$ anomaly are also addressed. The lightest Majorana fermions turn out to be potential dark matter candidates, made stable by suitable assignment of modular weights. The relic density of the same has been computed with annihilations mediated by inert scalars and new $U(1)$ gauge boson.