# Thermal Sunyaev-Zel'dovich Effect in the IGM due to Primordial Magnetic Fields

## TL;DR

This paper investigates how primordial magnetic fields influence the thermal Sunyaev-Zel'dovich effect in the intergalactic medium, showing that small-scale tSZ anisotropies can tightly constrain these early-universe magnetic fields.

## Contribution

It models the impact of primordial magnetic fields on IGM temperature fluctuations and tSZ power spectrum, highlighting their significance on small scales for constraining PMFs.

## Key findings

- tSZ power spectrum is significantly affected by PMFs on small scales
- Small-scale tSZ anisotropy measurements can tightly constrain primordial magnetic fields
- PMFs below current observational limits still produce detectable tSZ signals

## Abstract

In the present universe, magnetic fields exist with various strengths and on various scales. One possible origin of these cosmic magnetic fields is the primordial magnetic fields (PMFs) generated in the early universe. PMFs are considered to contribute to matter density evolution via Lorentz force and the thermal history of intergalactic medium (IGM) gas due to ambipolar diffusion. Therefore, information about PMFs should be included in the temperature anisotropy of the Cosmic Microwave Background through the thermal Sunyaev-Zel'dovich (tSZ) effect in IGM. In this article, given an initial power spectrum of PMFs, we show the spatial fluctuation of mass density and temperature of the IGM and tSZ angular power spectrum created by the PMFs. Finally, we find that the tSZ angular power spectrum induced by PMFs becomes significant on small scales, even with PMFs below the observational upper limit. Therefore, we conclude that the measurement of tSZ anisotropy on small scales will provide the most stringent constraint on PMFs.