Constraints on the Evolution of the Primordial Magnetic Field from the Small Scale CMB Angular Anisotropy

Recent observations of the cosmic microwave background (CMB) have extended measured the power spectrum to higher multipoles l &1000, and there appears to be possible evidence for excess power on small angular scales. The primordial magnetic field (PMF) can strongly affect the CMB power spectrum and the formation of large scale structure. In this paper, we calculate the CMB temperature anisotropies generated by including a power-law magnetic field at the photon last scattering surface (PLSS). We then deduce an upper limit on the primordial magnetic field based upon our theoretical analysis of the power excess on small angular scales. We have taken into account several important effects such as reionization and the modified matter sound speed in the presence of a magnetic field. An upper limit to the field strength of |Bλ| . 4.7 nG at the present scale of 1 Mpc is deduced. This is obtained by comparing the calculated theoretical result including the Sunyaev-Zeldovich (SZ) effect with recent observed data on the small scale CMB anisotropies from the Wilkinson Microwave Anisotropy Probe (WMAP), the Cosmic Background Imager (CBI) and the Arcminute Cosmology Bolometer Array Receiver (ACBAR). We discuss several possible mechanisms for the generation and evolution of the PMF. 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 Center for Astrophysics, Department of Physics, University of Notre Dame, Notre Dame, IN 46556, U.S.A.