In this thesis, we have shown that corrections due to the magnetic field background can produce circular polarization in CMB photons. The nucleon-nucleon scattering in a large magnetic background is considered to find its potential to change the neutrino emissivity of the neutron stars. For this purpose, we consider the one-pion-exchange approximation to find the nucleon-nucleon cross section in a background field as large as 10 15 –10 18 G. We show that the nucleon-nucleon cross section in neutron stars with temperatures in the range 0.1–5MeV can be changed up to the 1 order of magnitude with respect to the one in the absence of the magnetic field. Around B= 10 18 G the emissivity changes about an order of magnitude with respect to its corresponding value without magnetic field. Furthermore, the enhancement on the emissivity is higher for the lower temperatures. We show that corrections due to magnetic field in speed of neutrino are much smaller than anomaly reported by OPERA experiment. By obtaining the mixing angle and square mass difference in large magnetic field of neutron star, we show that this magnetic field cannot be larger than 10 16 G. We show that the Lorentz violation parameters such as c µ? and d µ? can be generated by the magnetic background. We obtain c µ? and d µ? of the order of 10 -27 for a neutrino, we also obtain H µ? of the order of 10 -36 eV for an electron-neutrino and d µ? around 10 -17 for electron in a magnetic background about 1G. Although the obtained results for neutrino is far from the experimental bounds, the magnetic field can produce the electron d µ? parameter as large as the current experimental bounds on this parameter. We have studied gravitational collapse of a compact star as a complete degenerate Fermi gas of neutrons, protons and electrons. We find fluxes of 10MeV electron- neutrinos and GeV electron and muon flavor neutrinos. The ratio of total muon flavor neutrinos to the total electron flavor neutrinos is computed at the source and after oscillation effects at the Earth, which is less than 1. We find that number of GeV antineutrino events in an ordinary detector such as Kamiokande is grater than 1 and total energy of neutrino flux is larger than 10 52 erg. Key Words : Magnetic field background, Circular polarization of the CMB radiation, Neutron star, Nucleon-nucleon scattering, Neutrino emissivity, Speed of neutrino, Neutrino oscillation, Gravitational collapse, High-energy neutrinos.
