# Secondary CMB temperature anisotropies from magnetic reheating

## TL;DR

This paper explores how inhomogeneous magnetic reheating from primordial magnetic fields affects CMB temperature anisotropies, providing new constraints on magnetic field properties and their coupling to curvature perturbations.

## Contribution

It introduces the concept of inhomogeneous magnetic reheating as a source of secondary CMB anisotropies and derives new observational bounds on the non-linear coupling parameter $b_{NL}$.

## Key findings

- Current CMB data constrain $b_{NL}$ to be less than approximately -36.5 for typical magnetic field parameters.
- Inhomogeneous magnetic reheating probes a wider range of scales than previous spectral distortion methods.
- Constraints are significantly stronger than future forecasts based solely on spectral distortion anisotropy measurements.

## Abstract

Spatially fluctuating primordial magnetic fields (PMFs) inhomogeneously reheat the Universe when they dissipate deep inside the horizon before recombination. Such an energy injection turns into an additional photon temperature perturbation. We investigate secondary cosmic microwave background (CMB) temperature anisotropies originated from this mechanism, which we call {\it inhomogeneous magnetic reheating}. We find that it can bring us information about non-linear coupling between PMFs and primordial curvature perturbations parametrized by $b_{\rm NL}$, which should be important for probing the generation mechanism of PMFs. In fact, by using current CMB observations, we obtain an upper bound on the non-linear parameter as $\log (b_{\rm NL} (B_{\lambda}/{\rm nG})^2) \lesssim {-36.5n_{B} - 94.0}$ with $B_{\lambda}$ and $n_{\rm B}$ being a magnetic field amplitude smoothed over $\lambda=1\; {\rm Mpc}$ scale and a spectral index of the PMF power spectrum, respectively. Our constraints are far stronger than a previous forecast based on the future CMB spectral distortion anisotropy measurements because inhomogeneous magnetic reheating covers a much wider range of scales, i.e., $1\; {\rm Mpc}^{-1} \lesssim k\lesssim 10^{15}\; {\rm Mpc}^{-1}$.