Neutrinos in Cosmology and Particle Physics

This thesis discusses two independent research topics. We first study keV sterile neutrinos as a Warm Dark Matter (WDM) candidate, focusing on their production at temperatures of the electroweak scale and the linear structure growth of WDM particles with arbitrary\ud distribution functions and masses of keV scale. At temperatures of the electroweak scale, the medium effect modifies the mixing angle between sterile and active neutrinos, introducing two narrow Mikheev-Smirnov-Wolfenstein (MSW) resonances that break adiabaticity and\ud enhance the non-thermal production of sterile neutrinos at small momenta. One of the two MSW resonances is in the absence of a lepton asymmetry and occurs only at temperatures around the electroweak scale. By solving the linearized collision-less Boltzmann equation, we obtain a semi-analytical expression of the matter power spectrum for WDM particles with arbitrary distributions agreeing within a few percent error with results from Boltzmann codes. This matter power spectrum depends on the horizon size at matter-radiation equality and the free streaming wave vector kfs, function of mass and distribution of WDM particles. We discover WDM acoustic oscillations at small scales about k>=2k_fs and an Integrated Sachs-Wolfe (ISW) effect in the Radiation Dominant (RD) era which enhances the matter\ud power spectrum for k<=k_fs. A quasi-degeneracy between the mass and distribution function of WDM on the matter power spectrum is identified, suggesting an inherent ambiguity of\ud Lyman-alpha analysis to constrain WDM parameters. Secondly, based on the observation that neutrinos produced from decay via the charge current interaction are entangled with the\ud corresponding charged leptons, we re-investigate the theory of neutrino oscillations with the focus of the dynamics of the entangled state. We study the dynamics of entanglement and dis-entanglement explicitly in time, which leads to non-conventional expressions for neutrino oscillation amplitudes and probabilities suggesting possible corrections for short baseline neutrino oscillation experiments. By applying this method to the GSI anomaly, we\ud unambiguously show that the GSI anomaly is not a consequence of neutrino oscillations