Constraining Primordial Magnetic Field from CMB Anisotropies at Higher Multipoles

The cosmological magnetic field is one of the important physical quantities which affect strongly the cosmic microwave background (CMB) power spectrum. Recent CMB observations have been extended to higher multipoles l &1000, and they resultantly exhibit an excess power than the standard model prediction in cosmological theory which best fits the Wilkinson Microwave Anisotropy Probe (WMAP) data at lower multipoles l .800. We calculate the CMB temperature anisotropies generated by the power-law magnetic field at the last scattering surface (LSS) in order to remove the tension between theory and observation at higher multipoles and also place a conservative upper limit on primordial magnetic field. In our present calculation we take account of the effects of reionization and ionization ratio exactly without approximation. These effects are very crucial to precisely estimate the effect of magnetic field on CMB power spectrum. We found that the primordial magnetic field which has the field strength Bλ ∼10nG and power-law spectral index n .0 offers a solution to the tension at high multipoles. Inferred upper limit to the field strength turns out to be |B| . 18 nG at 1Mpc, which is obtained by comparing the calculated theoretical result including the Sunyaev-Zeldovich (SZ) effect with recent WMAP data of the CMB anisotropies. Subject headings: cosmology: cosmic microwave background — methods: numerical — magnetic field Department of Astronomy, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan Division of Theoretical Astronomy, National Astronomical Observatory Japan, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan