Probing correlations of early magnetic fields using mu-distortion

TL;DR

This paper explores how early magnetic fields influence CMB spectral distortions and their correlations with temperature anisotropies, providing a new way to probe magnetogenesis models through mu-distortion measurements.

Contribution

It introduces a method to detect correlations between magnetic fields and curvature perturbations via mu-distortion and analyzes the potential of future experiments to constrain magnetogenesis.

Findings

A PIXIE-like experiment could detect magnetic fields of around 10 nG if the correlation parameter is order unity.

The correlation signal depends on the magnetic field strength and the non-Gaussianity parameter $b_{NL}$.

Magnetic fields from inflation could induce additional curvature bispectra, affecting the correlation analysis.

Abstract

The damping of a non-uniform magnetic field between the redshifts of about $10^4$ and $10^6$ injects energy into the photon-baryon plasma and causes the CMB to deviate from a perfect blackbody spectrum, producing a so-called $\mu$-distortion. We can calculate the correlation $\langle\mu T\rangle$ of this distortion with the temperature anisotropy $T$ of the CMB to search for a correlation $\langle B^2\zeta\rangle$ between the magnetic field $B$ and the curvature perturbation $\zeta$; knowing the $\langle B^2\zeta\rangle$ correlation would help us distinguish between different models of magnetogenesis. Since the perturbations which produce the $\mu$-distortion will be much smaller scale than the relevant density perturbations, the observation of this correlation is sensitive to the squeezed limit of $\langle B^2\zeta\rangle$, which is naturally parameterized by $b_{\text{NL}}$ (a parameter defined analogously to $f_{\text{NL}}$). We find that a PIXIE-like CMB experiments has a signal to noise $S/N\approx 1.0 \times b_{\text{NL}} (\tilde B_\mu/10\text{ nG})^2$, where $\tilde B_\mu$ is the magnetic field's strength on $\mu$-distortion scales normalized to today's redshift; thus, a 10 nG field would be detectable with $b_{\text{NL}}=\mathcal{O}(1)$. However, if the field is of inflationary origin, we generically expect it to be accompanied by a curvature bispectrum $\langle\zeta^3\rangle$ induced by the magnetic field. For sufficiently small magnetic fields, the signal $\langle B^2 \zeta\rangle$ will dominate, but for $\tilde B_\mu\gtrsim 1$ nG, one would have to consider the specifics of the inflationary magnetogenesis model. We also discuss the potential post-magnetogenesis sources of a $\langle B^2\zeta\rangle$ correlation and explain why there will be no contribution from the evolution of the magnetic field in response to the curvature perturbation.