# Milli-charged fermion vacuum polarization in cosmic magnetic fields and generation of CMB elliptic polarization

## TL;DR

This paper investigates how vacuum polarization caused by milli-charged fermions in cosmic magnetic fields can generate elliptic polarization in the CMB, providing analytic formulas and potential observational implications.

## Contribution

It presents the first detailed analysis of milli-charged fermion vacuum polarization effects on CMB polarization, including exact solutions and observational estimates.

## Key findings

- Circular polarization of CMB could reach 10^{-10} to 10^{-6}
- CMB polarization can be generated even from thermal equilibrium
- Limits on cosmic magnetic fields are derived from polarization data

## Abstract

The contribution of one loop milli-charged fermion vacuum polarization in cosmic magnetic field to the cosmic microwave background (CMB) polarization is considered. Exact and perturbative solution of the density matrix equations of motion in terms of the Stokes parameters are presented. For linearly polarized CMB at decoupling time, it is shown that propagation of CMB photons in cosmic magnetic field would generate elliptic polarization (circular and linear) of the CMB due to milli-charged fermion vacuum polarization. Analytic expressions for the degree of circular polarization and rotation angle of polarization plane of the CMB are presented. Depending on the ratio of milli-charged fermion relative charge to mass, $\epsilon/m_\epsilon$, and CMB observation frequency, it is shown that the acquired CMB degree of circular polarization could be of the order of magnitude $P_C(T_0)\sim 10^{-10}- 10^{-6}$ in the best scenario. The effect studied generates CMB polarization even in the case when the CMB is initially in thermal equilibrium. Limits on the magnetic field amplitude due to prior decoupling CMB polarization are presented.