Acoustic signatures in the Cosmic Microwave Background bispectrum from
  primordial magnetic fields
  Using the full radiation transfer function, we numerically calculate the CMB
angular bispectrum seeded by the compensated magnetic scalar density mode. We
find that, for the string inspired primordial magnetic fields characterized by
index $n_B=-2.9$ and mean-field amplitude $B_{\lam}=9{\rm nG}$, the angular
bispectrum is dominated by two primordial magnetic shapes. The first magnetic
shape looks similar to the one from local-type primordial curvature
perturbations, so both the amplitude and profile of the Komatsu-Spergel
estimator (reduced bispectrum) seeded by this shape are almost the same as
those of the primary CMB anisotropies. However, for different parameter sets
($l_1,l_2$), this "local-type" reduced bispectrum oscillates around different
asymptotic values in the high-$l_3$ regime because of the effect of the Lorentz
force, which is exerted by the primordial magnetic fields on the charged
baryons. This feature is different from the standard case where all modes
approach to zero asymptotically in the high-$l$ limit. On the other hand, the
second magnetic shape appears only in the primordial magnetic field model. The
amplitude of the Komatsu-Spergel estimator sourced by the second shape diverges
in the low-$l$ regime because of the negative slope of shape. In the high-$l$
regime, this amplitude is approximately equal to that of the first estimator,
but with a reversal phase.
