Computation approach for CMB bispectrum from primordial magnetic fields

TL;DR

This paper develops a detailed computational method to evaluate the CMB bispectrum caused by primordial magnetic fields, incorporating full angular dependence and analyzing various spectral indices to improve understanding of magnetic field effects on the early universe.

Contribution

It introduces a comprehensive calculation approach for the CMB bispectrum from primordial magnetic fields, including angular dependence and spectral index variations, advancing previous simplified models.

Findings

Explicitly derived the angle-averaged form of the bispectrum

Demonstrated the method's applicability to different spectral indices

Confirmed the rotational invariance of the bispectrum description

Abstract

We present a detailed calculation of our previous short paper [M. Shiraishi, D. Nitta, S. Yokoyama, K. Ichiki, and K. Takahashi, Phys. Rev. D 82, 121302 (2010).] in which we have investigated a constraint on the magnetic field strength through comic microwave background temperature bispectrum of vector modes induced from primordial magnetic fields. By taking into account full angular dependence of the bispectrum with spin spherical harmonics and Wigner symbols, we explicitly show that the cosmic microwave background bispectrum induced from the statistical-isotropic primordial vector fluctuations can be also described as an angle-averaged form in the rotationally invariant way. We also study the cases with different spectral indices of the power spectrum of the primordial magnetic fields.