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 $|B_{\lambda }|=0.85\pm 1.25(\pm 1\sigma )\mathrm{nG}$ on a comoving scale of at 1 Mpc, corresponding to upper limits of $<\mathbf{2.10}\mathrm{nG}$ (68% CL) and $<\mathbf{2.98}\mathrm{nG}$ (95% CL). While for the power spectral index we find $n_B=-{2.37}_{-0.73}^{+0.88}(\pm 1\sigma )$, corresponding to upper limits of $<-\mathbf{1.19}$ (68% CL) and $<-\mathbf{0.25}$ (95% 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.

Figure 1

Probability distributions and contours of $1\sigma$ and $2\sigma$ confidence limits for the standard cosmological parameters as a function of the PMF field strength $|B_{\lambda }|$ and power-law index $n_B$. Blue contours show $1\sigma$ (68%) confidence limits and sky blue contours show $2\sigma$ (95%) confidence limits. Red curves in the middle and bottom of the figure show the probability distributions of each parameter. Note the existence of a maximum in the probability distributions for $|B_{\lambda }|$ and $n_B$. The standard cosmological parameters do not have a degeneracy with the PMF parameters because they are mainly constrained by the observed CMB data for $\ell <1000$ (up to the 2nd peak), while the PMF is mainly influenced by the power on smaller angular scales and higher multipoles, $\ell >1000$.

Figure 2

Probability distributions and contours of $1\sigma$ and $2\sigma$ confidence limits for the parameters ${\sigma }_8$, $H_0$, $z_{\mathrm{reion}}$ and Age. Blue contours show $1\sigma$ (68%) confidence limits and sky blue contours show $2\sigma$ (95%) confidence limits. Red curves show probability distributions for each parameter. Note that these are not input priors, but output results.

Figure 3

Comparison of the best-fit computed total power spectrum with the observed CMB spectra. Plots show various ranges for: (a) TT ($2<\ell <2750$), (b) TT ($400<\ell <2750$) and (c) BB ($2<\ell <2750$) modes. Blue regions are from the best-fit parameter set and allowed regions are from the constrained parameter set as Table . Red, black, blue, green, orange, and purple dots with error bars show WMAP 5 yr, ACBAR 08, Boomerang, CBI, CAPMAP, and DASI data, respectively. Downward arrows for the error bars on panel (c) indicate that the data points are upper limits. Since the SZ effect depends upon the frequencies of the CMB for the TT mode, we plot the best fit and allowed regions in panels 3a, 3b surrounded by the curves with the SZ effect at the K (22.8 GHz) band (upper curves) and without the SZ effect (lower curves). Since the BB mode is not affected by the SZ effect, the upper curves and lower curves in panel 3(c) are defined by the constrained cosmological parameters of Table .