3+1 neutrino mixings model with $A_4$ triplet Majorana neutrino

We study a 3+1 active-sterile neutrino mixings model using an $A_4$ triplet right-handed neutrino ${\nu }_R$ and a singlet eV-scale sterile neutrino under $A_4\times Z_3\times Z_2$ discrete symmetry. Four scalar flavons are considered to reproduce neutrino oscillation parameters within the experimental 3$\sigma$ range. The model also studies the effective mass parameter in neutrinoless double beta decay experiments. Deviation from $\mu -\tau$ symmetry in the active neutrino mass matrix is generated through an antisymmetric interaction of ${\nu }_R$. This model successfully explains active-sterile neutrino mixings consistent with the cosmological upper bound on the sum of active neutrino mass $\sum m_i<0.113$ eV (0.145 eV) in NH(IH).