  We investigate the effects of the background primordial magnetic field (PMF)
on the cosmic microwave background (CMB). The sound speed of the tightly
coupled photon-baryon fluid is increased by the background PMF. The increased
sound speed causes the odd peaks of the CMB temperature fluctuations to be
suppressed and the CMB peak positions to be shifted to a larger scale. The
background PMF causes a stronger decaying potential and increases the amplitude
of the CMB. These two effects of the background PMF on a smaller scale cancel
out, and the overall effects of the background PMF are the suppression of the
CMB around the first peak and the shifting of peaks to a large scale. We also
discuss obtaining information about the PMF generation mechanisms, and we
examine the nonlinear evolution of the PMF by the constraint on the maximum
scale for the PMF distributions. Finally, we discuss degeneracies between the
PMF parameters and the standard cosmological parameters.
