Effects of a primordial magnetic field with log-normal distribution on
  the cosmic microwave background
  We study the effect of primordial magnetic fields (PMFs) on the anisotropies
of the cosmic microwave background (CMB). We assume the spectrum of PMFs is
described by log-normal distribution which has a characteristic scale, rather
than power-law spectrum. This scale is expected to reflect the generation
mechanisms and our analysis is complementary to previous studies with power-law
spectrum. We calculate power spectra of energy density and Lorentz force of the
log-normal PMFs, and then calculate CMB temperature and polarization angular
power spectra from scalar, vector, and tensor modes of perturbations generated
from such PMFs. By comparing these spectra with WMAP7, QUaD, CBI, Boomerang,
and ACBAR data sets, we find that the current CMB data set places the strongest
constraint at $k\simeq 10^{-2.5}$ Mpc$^{-1}$ with the upper limit $B\lesssim 3$
nG.
