Constraints on the Evolution of the Primordial Magnetic Field from the Small‐Scale Cosmic Microwave Background Angular Anisotropy

Abstract

Recent observations of the cosmic microwave background (CMB) have extendedthe measured power spectrum to higher multipoles $l\gtrsim$1000, and thereappears to be possible evidence for excess power on small angular scales. Theprimordial magnetic field (PMF) can strongly affect the CMB power spectrum andthe formation of large scale structure. In this paper, we calculate the CMBtemperature anisotropies generated by including a power-law magnetic field atthe photon last-scattering surface (PLSS). We then deduce an upper limit on thePMF based on our theoretical analysis of the power excess on small angularscales. We have taken into account several important effects such as themodified matter sound speed in the presence of a magnetic field. An upper limitto the field strength of $|B_\lambda|\lesssim$ 4.7 nG at the present scale of 1Mpc is deduced. This is obtained by comparing the calculated theoretical resultincluding the Sunyaev-Zeldovich (SZ) effect with recent observed data on thesmall-scale CMB anisotropies from the $Wilkinson Microwave Anisotropy Probe$(WMAP), the Cosmic Background Imager (CBI), and the Arcminute CosmologyBolometer Array Receiver (ACBAR). We discuss several possible mechanisms forthe generation and evolution of the PMF.