Modular A4 symmetry in 3+1 active–sterile neutrino masses and mixings

Motivated by the significance of modular symmetry in generating neutrino masses and flavor mixings, we apply the modular [Formula: see text] symmetry in a [Formula: see text] scheme of active–sterile neutrino mixings. Neutrino oscillation observables in the 3[Formula: see text] range are successfully reproduced through the vacuum expectation value of the modulus [Formula: see text]. We also study phenomenologies related to the effective neutrino masses [Formula: see text] in tritium beta decay and [Formula: see text] in neutrinoless double beta decay. Mixings between active neutrinos and eV scale sterile neutrino are analyzed in detail. The model also predicts the Dirac CP-violating phase [Formula: see text] and Majorana phases [Formula: see text] and [Formula: see text]. The best-fit values of the neutrino mixing angles and ratios of two mass-squared differences are determined using minimum [Formula: see text] analysis. The best-fit values of the neutrino oscillation observables are predicted as [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] for NH while [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] for IH. We also observe that the predictions of effective neutrino mass parameters in the [Formula: see text] scheme are significantly different from the three neutrino paradigm.