New Constraints on the Primordial Magnetic Field
  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.
