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Primordial magnetic fields lead to non-Gaussian signals in the Cosmic Microwave Background (CMB) even at the lowest order, as magnetic stresses, and the temperature anisotropy they induce, depend quadratically on the magnetic field.
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The WMAP 5-year data gives limits on primordial non-Gaussianity − 9 < f N L l o c a l < 111 -9<f_{NL}^{local}<111 and − 151 < f N L e q u i l < 253 -151<f_{NL}^{equil}<253 at the 95 % 95\% confidence level for the local and equilateral models, respectively. Of course these limits use the much larger range of l l values than the range for which the SW contribution is important
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D. Paoletti, F. Finelli and F. Paci, arxiv:0811.0230 (2008)
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C. Caprini, F. Finelli, D. Paoletti and A. Riotto, arxiv:0903.1420 (2009)
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