Parity violation of primordial magnetic fields in the CMB bispectrum

Abstract

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 ${\sum }_{n=1}^3{\ell }_n=\mathrm{odd}$. 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, we find that assuming the generation of the nearly scale-invariant non-helical and helical PMFs from the grand unification energy scale ($10^{14}\mathrm{GeV}$) to the electroweak one ($10^3\mathrm{GeV}$), the intensity-intensity-intensity bispectrum for ${\sum }_{n=1}^3{\ell }_n=\mathrm{odd}$ can be observed by the WMAP experiment under the condition that $B_{1\mathrm{Mpc}}^{2/3}{\mathcal{B}}_{1\mathrm{Mpc}}^{1/3}>2.7-4.5\mathrm{nG}$ with $B_{1\mathrm{Mpc}}$ and ${\mathcal{B}}_{1\mathrm{Mpc}}$ being the non-helical and helical PMF strengths smoothed on 1 Mpc, respectively.

Comments: 18 pages, 2 figures. Accepted for publication in JCAP