Power spectrum of post-inflationary primordial magnetic fields

The origin of large scale magnetic fields is one of the most puzzling topics in cosmology and astrophysics. It is assumed that the observed magnetic fields result from the amplification of an initial field produced in the early universe. In this paper we compute the exact power spectrum of magnetic fields created after inflation best known as post inflationary magnetic fields, using the first order cosmological perturbation theory. Our treatment differs from others works because we include an infrared cutoff which encodes only causal modes in the spectrum. The cross-correlation between magnetic energy density with Lorentz force and the anisotropic part of the electromagnetic field are exactly computed. We compare our results with previous works finding agreement in cases where the ratio between lower and upper cutoff is very small. However, we found that spectrum is strongly affected when this ratio is greater than 0.2. Moreover, the effect of a post inflationary magnetic field with a lower cutoff on the angular power spectrum in the temperature distribution of CMB was also exactly calculated. The main feature is a shift of the spectrum's peak as function of the infrared cutoff, therefore analyzing this effect we could infer the value of this cutoff and thus constraining the primordial magnetic fields generation models.