Aprimordial magnetic field (PMF) would be expected to manifest itself in the cosmic microwave background (CMB) temperature and polarization anisotropies, and also in the forma-tion of large scale structure(LSS). In this article, we demonstrate how the PMF is an important cosmological physical process on small scales as follows, We also report the newest constraints on the PMF amplitude B_λ and the power spectral index n_B which have been deduced from the available CMB observational data by using our computational framework and the Markov chain Monte Carlo method. In particular we find that |B_λ|, < 2.10(68%CL) nG and < 2.98(95%CL) nG and n_B< —1.19(68%CL) and < —0.25(95%CL) at a present scale of 1 Mpc.
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