Cosmic Microwave Background Trispectrum and Primordial Magnetic Field Limits

Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics

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5 pages

Scientific paper

Primordial magnetic fields will generate non-Gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-Gaussianity, the CMB trispectrum $T^{l_{_1}l_{_2}}_{l_{_3}l_{_4}}$, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of $T^{l_{_1}l_{_2}}_{l_{_3}l_{_4}} \approx 5 \times 10^{-30}$ and $T^{l_{_1}l_{_2}}_{l_{_3}l_{_4}} \approx 10^{-19}$, respectively. Observational limits on CMB non-Gaussianity from WMAP7 data allow us to set sub-nanoGauss upper limits of $B_0 \lesssim 0.7 $ nG on the present value of the primordial cosmic magnetic field. This represents the tightest limit so far on the strength of primordial magnetic fields, on megaparsec scales, better than limits from the CMB bispectrum and all modes in the CMB power spectrum. Thus, the CMB trispectrum is a new and more sensitive probe of primordial magnetic fields on large scales.

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