Common Origin of Non-zero $theta_{13}$ and Baryon Asymmetry of the Universe in a TeV scale Seesaw Model with $A_4$ Flavour Symmetry

We study the possibility of generating non-zero reactor mixing angle $theta_{13}$ and baryon asymmetry of the Universe within the framework of an $A_4$ flavour symmetric model. Using the conventional type I seesaw mechanism we construct the Dirac and Majorana mass matrices which give rise to the correct light neutrino mass matrix. Keeping the right handed neutrino mass matrix structure trivial so that it gives rise to a (quasi) degenerate spectrum of heavy neutrinos suitable for resonant leptogenesis at TeV scale, we generate the non-trivial structure of Dirac neutrino mass matrix that can lead to the light neutrino mixing through type I seesaw formula. Interestingly, such a setup naturally leads to non-zero $theta_{13}$ due to the existence of anti-symmetric contraction of the product of two triplet representations of $A_4$. Such antisymmetric part of triplet products usually vanish for right handed neutrino Majorana mass terms, leading to $mu-tau$ symmetric scenarios in the most economical setups. We constrain the model parameters from the requirement of producing the correct neutrino data as well as baryon asymmetry of the Universe for right handed neutrino mass scale around TeV. The $A_4$ symmetry is augmented by additional $Z_3 times Z_2$ symmetry to make sure that the splitting between right handed neutrinos required for resonant leptogenesis is generated only by next to leading order terms, making it naturally small. We find that the inverted hierarchical light neutrino masses give more allowed parameter space consistent with neutrino and baryon asymmetry data.