Parity violation of primordial magnetic fields in the CMB bispectrum

Details Parity violation of primordial magnetic fields in the CMB bispectrum Parity violation of primordial magnetic fields in the CMB bispectrum

2012-02-13

arxiv.org/abs/1202.2847v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

18 pages, 2 figures. Submitted to JCAP

Scientific paper

We study the parity violation in the cosmic microwave background (CMB) bispectrum induced by primordial magnetic fields (PMFs). Deriving a general formula for the CMB bispectrum generated from not only non-helical but also helical PMFs, we find that helical PMFs produce characteristic signals, which disappear in parity-conserving cases, such as the intensity-intensity-intensity bispectra arising from $\sum_{n=1}^3 \ell_n = {\rm odd}$. For fast numerical calculation of the CMB bispectrum, we reduce the one-loop formula to the tree-level one by using the so-called pole approximation. Then, we show that the magnetic anisotropic stress, which depends quadratically on non-helical and helical PMFs and acts as a source of the CMB fluctuation, produces the local-type non-Gaussianity. Comparing the CMB bispectra composed of the scalar and tensor modes with the noise spectra determined by the cosmic variance, we find that assuming the generation of the nearly scale-invariant non-helical and helical PMFs from the grand unification energy scale ($10^{14} {\rm GeV}$) to the electroweak one ($10^{3} {\rm GeV}$), the intensity-intensity-intensity bispectrum for $\sum_{n=1}^3 \ell_n = {\rm odd}$ can be observed under the condition that $B_{1 \rm Mpc}^{2/3} {\cal B}_{1 \rm Mpc}^{1/3} > 2.7 - 4.5 {\rm nG}$ with $B_{1 \rm Mpc}$ and ${\cal B}_{1 \rm Mpc}$ being the non-helical and helical PMF strengths smoothed on 1 Mpc, respectively.

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