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The present work is inspired by the application of $A_4$ modular symmetry inthe linear seesaw framework, which restricts the use of multiple flavon fields.Linear seesaw is realized with six heavy $SU(2)_L$ singlet fermion superfieldsand a weighton in a supersymmetric framework. The non-trivial transformation ofYukawa couplings under the $A_4$ modular symmetry helps to explore the neutrinophenomenology with a specific flavor structure of the mass matrix. We discussthe phenomena of neutrino mixing and show that the obtained mixing angles andCP violating phase in this framework are compatible with the observed $3\sigma$range of the current oscillation data. In addition, we also investigate thenon-zero CP asymmetry from the decay of lightest heavy fermion superfield toexplain the preferred phenomena of baryogenesis through leptogenesis includingflavor effects.

Implications of $A_4$ modular symmetry on Neutrino mass, Mixing and Leptogenesis with Linear Seesaw