Neutrino model in left-right symmetric linear seesaw augmented with $$A_4$$ modular group

Abstract In this work, we have invoked $$A_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> modular symmetry in the left-right symmetric linear seesaw model. Interestingly, such modular symmetry restricts the proliferation of flavon fields, and as a result, the predictability of the model is enhanced. The fermion sector of the model comprises quarks, leptons, and a sterile fermion in each generation, while the scalar sector consists of Higgs doublets and bidoublets. We investigate numerically various Yukawa coupling coefficients, the neutrino masses and mixing parameters in our intended model and predictions become consistent with the $$3\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> range of current neutrino oscillation data. We also studied the non-unitarity, effects on lepton flavor violation in our model and evolution of lepton asymmetry to explain the current baryon asymmetry of the universe.