  The primordial magnetic field (PMF) can strongly affect the cosmic microwave
background (CMB) power spectrum and the formation of large scale structure. In
this presentation, 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 the modified matter
sound speed in the presence of a magnetic field. An upper limit to the field
strength of $|B_\lambda|\lesssim$ 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 before, during and after the BBN.
