We present the newest statistical and numerical analysis of the matter and cosmic microwave background power spectrum with effects of the primordial magnetic field ( PMF ) included .
New limits to the PMF strength and power spectral index are obtained based upon the accumulated data for both the matter and CMB power spectra on small angular scales .
We find that a maximum develops in the probability distribution for a magnitude of the PMF of |B _ { \lambda } | = 0.85 \pm 1.25 ( \pm 1 \sigma ) nG on a comoving scale of at 1 Mpc , corresponding to upper limits of \mathbf { < 2.10 nG } ( 68 \% \mathrm { CL } ) and \mathbf { < 2.98 nG } ( 95 \% \mathrm { CL } ) .
While for the power spectral index we find n _ { \mathrm { B } } = -2.37 ^ { +0.88 } _ { -0.73 } ( \pm 1 \sigma ) , corresponding to upper limits of \mathbf { < -1.19 } ( 68 \% \mathrm { CL } ) and \mathbf { < -0.25 } ( 95 \% \mathrm { CL } ) .
This result provides new constraints on models for magnetic field generation and the physics of the early universe .
We conclude that future observational programs for the CMB and matter power spectrum will likely provide not only upper limits but also lower limits to the PMF parameters .