Cosmic microwave background bispectrum of tensor passive modes induced from primordial magnetic fields

TL;DR

This paper calculates the CMB bispectrum caused by tensor passive modes induced by primordial magnetic fields, providing estimates that constrain the magnetic field strength based on non-Gaussianity observations.

Contribution

It introduces a novel computation of the CMB bispectrum from tensor passive modes generated by primordial magnetic fields, linking magnetic field strength to observable non-Gaussian signals.

Findings

Estimated the bispectrum magnitude for nearly scale-invariant magnetic spectra.

Derived constraints on primordial magnetic field strength from bispectrum measurements.

Quantified the dependence of bispectrum amplitude on magnetic field energy scale.

Abstract

If the seed magnetic fields exist in the early Universe, tensor components of their anisotropic stresses are not compensated prior to neutrino decoupling and the tensor metric perturbations generated from them survive passively. Consequently, due to the decay of these metric perturbations after recombination, the so-called integrated Sachs-Wolfe effect, the large-scale fluctuations of CMB radiation are significantly boosted. This kind of CMB anisotropy is called the "tensor passive mode." Because these fluctuations deviate largely from the Gaussian statistics due to the quadratic dependence on the strength of the Gaussian magnetic field, not only the power spectrum but also the higher-order correlations have reasonable signals. With these motives, we compute the CMB bispectrum induced by this mode. When the magnetic spectrum obeys a nearly scale-invariant shape, we obtain an estimation of a typical value of the normalized reduced bispectrum as $\ell_1(\ell_1 + 1)\ell_3(\ell_3+1)|b_{\ell_1\ell_2\ell_3}| \sim (130-6) \times 10^{-16} (B_{1 \rm Mpc} / 4.7 {\rm nG})^6$ depending on the energy scale of the magnetic field production from $10^{14}$GeV to $10^3$GeV. Here, $B_{1 {\rm Mpc}}$ is the strength of the primordial magnetic field smoothed on $1 {\rm Mpc}$. From the above estimation and the current observational constraint on the primordial non-Gaussianity, we get a rough constraint on the magnetic field strength as $B_{1 {\rm Mpc}} < 2.6 - 4.4 {\rm nG}$.