Pranjal Trivedi, T. R. Seshadri, Kandaswamy Subramanian
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.
View original:
http://arxiv.org/abs/1111.0744
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