We construct a neutrino mass model based on the flavour symmetry group A4×C4×C6×C2 which accommodates a light sterile neutrino in the minimal extended seesaw (MES) scheme. Besides the flavour symmetry, we introduce a U(1) gauge symmetry in the sterile sector and also impose CP symmetry. The vacuum alignments of the scalar fields in the model spontaneously break these symmetries and lead to the construction of the fermion mass matrices. With the help of the MES formulas, we extract the light neutrino masses and the mixing observables. In the active neutrino sector, we obtain the TM2 mixing pattern with non-zero reactor angle and broken μ-τ reflection symmetry. We express all the active and the sterile oscillation observables in terms of only four real model parameters. Using this highly constrained scenario we predict $$ {\sin}^2{\theta}_{23}={0.545}_{-0.004}^{+0.003},\sin \delta =-{0.911}_{-0.005}^{+0.006},{\left|{U}_{e4}\right|}^2={0.029}_{-0.008}^{+0.009},{\left|{U}_{\mu 4}\right|}^2={0.010}_{-0.003}^{+0.003}\kern0.5em \mathrm{and}\kern0.5em {\left|{U}_{\tau 4}\right|}^2={0.006}_{-0.002}^{+0.002} $$ sin 2 θ 23 = 0.545 − 0.004 + 0.003 , sin δ = − 0.911 − 0.005 + 0.006 , U e 4 2 = 0.029 − 0.008 + 0.009 , U μ 4 2 = 0.010 − 0.003 + 0.003 and U τ 4 2 = 0.006 − 0.002 + 0.002 which are consistent with the current data.

We use S 4 discrete group to construct a neutrino flavour model which leads to T M 1 mixing and is consistent with the neutrino oscillation data. Using the model's constrained parameter space, we predict the values of Dirac CP phase and the light neutrino mass as −1 < sin δ < −0.9 and 1.7 < m 1 (meV) < 5.5 respectively. We thoroughly examine the usefulness of this model in explaining the observed baryon asymmetry of the Universe. Near-maximal breaking of CP symmetry (arising due to the TM 1 constraint) helps us in generating adequate baryon asymmetry through leptogenesis. We study the evolution of the asymmetry (generated due to the decay of the heavy Majorana neutrinos) starting from the primordial Universe in two different ways (i)explicitly solving network of Boltzmann equations, (ii) using approximate analytic solution and we have shown the extent of their equivalence. Nearly accurate analytical fits are used thereafter to evaluate baryon asymmetry for the whole parameter space allowed by 3σ global fit of oscillation data and to impose a constraint on the yet unbounded mass scale parameter of Dirac neutrino mass matrix. Furthermore, significant contribution of N 2 decay in the context of flavoured leptogenesis is also estimated.

In 2004, two of us proposed a texture, the "Simplest" neutrino mass matrix, which predicted sin θ 13 = 2∆m 2 sol /3∆m 2 atm and δ CP = 90 • . Using today's measured values for neutrino mass-squared differences, this prediction gives sin 2 2θ 13 0.086 +0.003 −0.006 , compared with a measured value, found by averaging the results of the Daya Bay and RENO experiments, of sin 2 2θ 13 = 0.093 ± 0.010. Here we present a specific model based on S 4 symmetry leading to this successful texture in the context of the type-1 see-saw mechanism, assuming Majorana neutrinos. In this case, slightly different predictions are obtained relating θ 13 to the light neutrino masses, which are in accord with current experimental limits and testable at future experiments. Large CP asymmetries remain a generic prediction of the texture.

A procedure for using the eigenvectors of the elements of the representations of a discrete group in model building is introduced and is used to construct a model that produces a large reactor mixing angle, sin 2 θ13 = 2 3 sin 2 π 16 , in agreement with recent neutrino oscillation observations. The model fully constrains the neutrino mass ratios and predicts normal hierarchy with the light neutrino mass, m1 ≈ 25 meV. Motivated by the model, a new mixing ansatz is postulated which predicts all the mixing angles within 1σ errors.