Constraints on Primordial Magnetic Fields from Planck combined with the South Pole Telescope CMB B-mode polarization measurements

A primordial magnetic field (PMF) present before recombination can leave specific signatures on the cosmic microwave background (CMB) fluctuations. Of particular importance is its contribution to the B-mode polarization power spectrum. Indeed, vortical modes sourced by the PMF can dominate the B-mode power spectrum on small scales, as they survive damping up to a small fraction of the Silk length. Therefore, measurements of the B-mode polarization at high-$\ell$ , such as the one recently performed by the South Pole Telescope (SPT), have the potential to provide stringent constraints on the PMF. We use the publicly released SPT B-mode polarization spectrum, along with the temperature and polarization data from the Planck satellite, to derive constraints on the magnitude, the spectral index and the energy scale at which the PMF was generated. We find that, while Planck data constrains the magnetic amplitude to $B_{1 \, \text{Mpc}} < 3.3$ nG at 95\% confidence level (CL), the SPT measurement improves the constraint to $B_{1 \, \text{Mpc}} < 1.5$ nG. The magnetic spectral index, $n_B$, and the time of the generation of the PMF are unconstrained. For a nearly scale-invariant PMF, predicted by simplest inflationary magnetogenesis models, the bound from Planck+SPT is $B_{1 \, \text{Mpc}} < 1.2$ nG at 95% CL. For PMF with $n_B=2$, expected for fields generated in post-inflationary phase transitions, the 95% CL bound is $B_{1 \, \text{Mpc}} < 0.002$ nG, corresponding to the magnetic fraction of the radiation density $\Omega_{B\gamma} < 10^{-3}$ or the effective field $B_{\rm eff} < 100$ nG. The patches for the Boltzmann code CAMB and the Markov Chain Monte Carlo engine CosmoMC, incorporating the PMF effects on CMB, are made publicly available.Comment: 12 pages, 9 figures, 4 table

The Search for a Primordial Magnetic Field

Magnetic fields appear wherever plasma and currents can be found. As such, they thread through all scales in Nature. It is natural, therefore, to suppose that magnetic fields might have been formed within the high temperature environments of the big bang. Such a primordial magnetic field (PMF) would be expected to arise from and/or influence a variety of cosmological phenomena such as inflation, cosmic phase transitions, big bang nucleosynthesis, the cosmic microwave background (CMB) temperature and polarization anisotropies, the cosmic gravity wave background, and the formation of large-scale structure. In this review, we summarize the development of theoretical models for analyzing the observational consequences of a PMF. We also summarize the current state of the art in the search for observational evidence of a PMF. In particular we review the framework needed to calculate the effects of a PMF power spectrum on the CMB and the development of large scale structure. We summarize the current constraints on the PMF amplitude $B_\lambda$ and the power spectral index $n_B$ and discuss prospects for better determining these quantities in the near future.Comment: 40 pages, 13 figures, Accepted for Physics Reports 23 Feb 2012. Available online 3 March 2012. In press, corrected proo

New Primordial-Magnetic-Field Limit from The Latest LIGO S5 data

Since the energy momentum tensor of a magnetic field always contains a spin-2 component in its anisotropic stress, stochastic primordial magnetic field (PMF) in the early universe must generate stochastic gravitational wave (GW) background. This process will greatly affect the relic gravitational wave (RGW), which is one of major scientific goals of the laser interferometer GW detections. Recently, the fifth science (S5) run of laser interferometer gravitational-wave observatory (LIGO) gave a latest upper limit $\Omega_{GW}<6.9\times10^{-6}$ on the RGW background. Utilizing this upper limit, we derive new PMF Limits: for a scale of galactic cluster $\lambda=1$ Mpc, the amplitude of PMF, that produced by the electroweak phase transition (EPT), has to be weaker than $B_{\lambda} \leq 4\times 10^{-7}$ Gauss; for a scale of supercluster $\lambda=100$ Mpc, the amplitude of PMF has to be weaker than $B_{\lambda} \leq 9\times 10^{-11}$ Gauss. In this manner, GW observation has potential to make interesting contributions to the study of primordial magnetic field.Comment: 17 pages, 3 figures, accepted for publication in PR

Comparison of The Kois Dento-Facial Analyzer System with an Earbow for Mounting a Maxillary Cast

Statement of problem: The Kois Dento-Facial Analyzer System (KDFA) is used by clinicians to mount maxillary casts and evaluate and treat patients. Limited information is available for understanding whether the KDFA should be considered as an alternative to an earbow. Purpose: The purpose of this study was to evaluate maxillary casts mounted using the KDFA with casts mounted using Panadent\u27s Pana-Mount Facebow (PMF). Both articulation methods were compared against a lateral cephalometric radiograph. Material and methods: Fifteen dried human skulls were used. Lateral cephalometric radiographs and 2 maxillary impressions were made of each skull. One cast from each skull was mounted on an articulator by means of the KDFA and the other by using the PMF. A standardized photograph of each articulation was made, and the distance from the articular center to the incisal edge position and the occlusal plane angle were measured. The distance from condylar center to the incisal edge and the occlusal plane angle were measured from cephalometric radiographs. Finally, the 3-dimensional position of each articulation was determined with a Panadent CPI-III. A randomized complete block design analysis of variance (RCBD) and post hoc tests (Tukey-Kramer HSD) (α=.05) were used to evaluate the occlusal plane angle and axis-central incisor distance. A paired 2-sample t test for means (α=.05) was used to compare the X, Y, and Z distance at the right and left condyle. Results: The KDFA and PMF mounted the maxillary cast in a position that was not statistically different from the skull when comparing the occlusal plane angle (P=.165). Both the KDFA and the PMF located the maxillary central incisor edge position in a significantly different position compared with the skull (P=.001) but were not significantly different from each other. The 3-dimensional location of the maxillary casts varied at the condyles by approximately 9 to 10.3 mm. Conclusion: The KDFA mounted the maxillary cast in a position that was not statistically different from the PMF when comparing the incisal edge position and the occlusal plane angle. Both the KDFA and the PMF located the maxillary incisal edge position in a significantly different position compared with the anatomic position on dried human skulls

CMB Constraints on a Stochastic Background of Primordial Magnetic Fields

We constrain a stochastic background of primordial magnetic field (PMF) by its contribution to the angular power spectrum of cosmic microwave background anisotropies. We parametrize such stochastic background by a power-law spectrum with index $n_B$ and by its Gaussian smoothed amplitude $B_\lambda$ on a comoving length $\lambda$. We give an approximation for the spectra of the relevant correlators of the energy-momentum of the stochastic background of PMF for any $n_B$. By using the WMAP 7 year data in combination with ACBAR, BICEP and QUAD we obtain the constraint $B_{1 {\rm Mpc}} < 5.0$ nG at 95% confidence level for a stochastic background of non-helical PMF. We discuss the relative importance of the scalar and vector contribution to CMB anisotropies in obtaining these constraints. We then forecast {\sc Planck} capabilities in constraining $B_{1 {\rm Mpc}}$.Comment: 13 pages, 7 figures, 3 tables. Revised version accepted for publication in Phys. Rev. D, conclusions unchange

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 $\mathbf{< 2.10 nG} (68$ and $\mathbf{< 2.98 nG} (95$. 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 $\mathbf{< -1.19} (68$ 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.Comment: 7 pages, 3 figures, 1 table, final version to appear in Phys. Rev. D, to match proof