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Abstract:

We propose a new method for constraining a primordial homogeneous magnetic field with the cosmic microwave background. Such a field will induce an observable parity odd cross correlation between the polarization anisotropy and the temperature anisotropy by Faraday rotation. We analyze the necessary experimental features to match, and improve, current constraints of such a field by measuring this correlation.

Abstract:

We derive an upper limit of $B_0<3.4\times 10^{-9}(\Omega_0h_{50}^2)^{1/2}$ Gauss on the present strength of any primordial homogeneous magnetic field. The microwave background anisotropy created by cosmological magnetic fields is calculated in the most general flat and open anisotropic cosmologies containing expansion-rate and 3-curvature anisotropies. Our limit is derived from a statistical analysis of the 4-year Cosmic Background Explorer data for anisotropy patterns characteristic of homogeneous anisotropy averaged over all possible sky orientations with respect to the COBE receiver. The limits we obtain are considerably stronger than those imposed by primordial nucleosynthesis and ensure that other magnetic field effects on the microwave background structure are unobservably small.

Abstract:

Gaussian cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-Gaussian skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We argue that this method is inefficient, due to the redundancy of information existing in the complete set of moments. In this paper we propose a set of new statistics or non-Gaussian spectra to be extracted out of the angular distribution of the Fourier transform of the temperature anisotropies in the small field limit. These statistics complement the power spectrum and act as localization, shape, and connectedness statistics. They quantify generic non-Gaussian structure, and may be used in more general image processing tasks. We concentrate on a subset of these statistics and argue that while they carry no information in Gaussian theories they may be the best arena for making predictions in some non-Gaussian theories. As examples of applications we consider superposed Gaussian and non-Gaussian signals, such as point sources in Gaussian theories or the realistic Kaiser-Stebbins effect. We show that in these theories non-Gaussianity is only present in a ring in Fourier space, which is best isolated in our formalism. Subtle but strongly non-Gaussian theories are also written down for which only non-Gaussian spectra may accuse non-Gaussianity.