Effects of Primordial Magnetic Fields on the CMB

Magnetic fields are observed on nearly all scales in the universe, from stars and galaxies upto galaxy clusters and even beyond. The origin of cosmic magnetic fields is still an open question, however a large class of models puts its origin in the very early universe. Observations of the cosmic microwave background (CMB) provide a window to the early universe and might therefore be able to tell us whether cosmic magnetic fields are of primordial, cosmological origin and at the same time constrain its parameters. I will concentrate on the effects of a stochastic magnetic field on scalar perturbations and present the resulting angular power spectra of the CMB temperature anisotropies and polarization as well as the linear matter power spectrum. Moreover, magnetic fields have an additional distinct signature as Faraday rotation induces a frequency dependent B-mode of the CMB polarization.