Magnetic fields from inflation: The CMB temperature anisotropies
  The cosmic microwave background (CMB) temperature anisotropies from
primordial magnetic fields are studied. In addition to the known passive and
the compensated mode we discuss an inflationary magnetic mode in the curvature
perturbation, present when magnetic fields are generated during inflation. This
mode is absent if the generation mechanism is causal, e.g. a phase transition.
We compute and discuss the effect of this mode on the observed CMB anisotropy
spectrum, in comparison with the passive and compensated ones. We find that it
dominates the CMB anisotropy, and consequently leads to stronger constraints on
the amplitude $B_{1\,{\rm Mpc}}$ and spectral index $n_B$ of the magnetic field
than what usually found in CMB analyses from the compensated mode. This happens
in particular for spectral indexes $n_B>-3$: the inflationary magnetic mode is
always scale invariant, therefore through this mode even a magnetic field with
a spectrum which is not scale invariant can leave a detectable signal in the
CMB at large scales.
