Topics in Neutrino Physics and Cosmology

This thesis focuses on timely issues in particle physics of neutrino phenomenology and cosmology. In this work, the methods of quantum optics, quantum field theory in curved spacetime and non-equilibrium field theory are employed to study the issues of inflation and neutrino mixing and oscillations in terrestrial and cosmological settings. Anomalies in short baseline oscillation experiments have provided hints of an additional neutrino species which are used as motivation to study potential experimental signatures through decays at rest, modifications to the treatment of appearance/disappearance oscillation experiments and experiments searching for lepton number violation. The role of decoherence and entanglement in the production mechanism of a two body decay is explored further in Minkowski and de Sitter spacetime with the aim of studying correlations in the CMB. This work is extended in Minkowski spacetime by studying decoherence issues in the cascade decay of successive two body decays with the aim of searching for new particles. The effect of initial conditions for inflation is explored with the motivation of persistent large scale anomalies and with an eye towards the soon-to-be-measured tensor to scalar ratio. Inclusion of these non-trivial initial conditions introduces large scale power suppression and potentially observable oscillations into the tensor to scalar ratio. The issue of dark matter is explored through the possibility of previously unstudied sources a sterile neutrino dark matter candidate. Pions, which are the most abundant particle after the QCD phase transition, can lead to the production of sterile neutrinos which yields a non negligible abundance of dark matter compared to established mechanisms in the literature. This additional source of sterile neutrino naturally leads to a multi component distribution function and a natural scenario for mixed dark matter. Furthersources of sterile neutrinos are discussed and the possibility of sterile neutrinos produced at electroweak temperatures is explored and leads to a generalized temperature dependence of active sterile mixing