Cosmic microwave background bispectrum of vector modes induced from primordial magnetic fields

TL;DR

This paper calculates the bispectrum of vector modes in the cosmic microwave background induced by primordial magnetic fields, analyzing its shape and amplitude to constrain magnetic field strength.

Contribution

It provides a detailed computation of the CMB bispectrum from vector modes due to primordial magnetic fields, including angular dependence and shape analysis.

Findings

Estimated bispectrum amplitude in the squeezed limit.

Projected magnetic field strength constraints from Planck data.

Quantified the bispectrum's shape dependence.

Abstract

We calculate the cosmic microwave background bispectrum of vector modes induced from primordial magnetic fields. We take into account the full angular dependence of the bispectrum and discuss the amplitude and also the shape of the bispectrum in $\ell$ space. In the squeezed limit as $\ell_1 = \ell_2 \gg \ell_3$, we estimate a typical values of the normalized reduced bispectrum as $\ell_1(\ell_1 + 1)\ell_3(\ell_3+1)|b_{\ell_1\ell_2\ell_3}| \sim 2 \times 10^{-19}$, for the strength of the primordial magnetic field smoothed on $1 {\rm Mpc}$ scale $B_{1 \rm Mpc} = 4.7 \rm nG$ assuming a nearly scale-invariant spectrum of magnetic fields. We find that a constraint on the magnetic field strength will be roughly estimated as $B_{1 \rm Mpc} < 10 {\rm nG}$ if PLANCK places a limit on the nonlinearity parameter of local-type configuration as $|f^{\rm local}_{\rm NL}| < 5$.