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.
