CMB anisotropies and linear matter power spectrum in models with non-thermal neutrinos and primordial magnetic fields

Angular power spectra of temperature anisotropies and polarization of the cosmic microwave background (CMB) as well as the linear matter power spectra are calculated for models with three light neutrinos with non-thermal phase-space distributions in the presence of a primordial stochastic magnetic field. The non-thermal phase-space distribution function is assumed to be the sum of a Fermi-Dirac and a gaussian distribution. It is found that the known effective description of the non-thermal model in terms of a twin thermal model with extra relativistic degrees of freedom can also be extended to models including a stochastic magnetic field. Numerical solutions are obtained for a range of magnetic field parameters.