CMB birefringence from ultra-light axion string networks

TL;DR

This paper develops an analytic framework to study the polarization rotation of CMB photons caused by ultralight axion string networks, revealing characteristic scales and signals that can inform axion properties.

Contribution

It introduces a new formalism and kernel function to calculate CMB birefringence correlations from arbitrary axion string networks, including simple loop distributions.

Findings

The angular correlation function peaks at a scale set by the loop size at recombination.

A characteristic birefringence power spectrum peak appears around a specific multipole moment.

Network collapse introduces an additional scale related to the axion mass.

Abstract

The polarization of Cosmic Microwave Background (CMB) photons is rotated as they pass through (ultralight-) axion string loops. Studying this birefringence can reveal valuable information about the axion-photon coupling and the structure of the string network. We develop an approximate analytic formalism and identify a kernel function that can be used to calculate the two-point correlation function for CMB birefringence induced by an arbitrary axion string network. Using this formalism, we evaluate the birefringence signal for some simple loop distributions (including scaling and network collapse). We find that the angular correlation function has a characteristic angular scale set by $\theta_\mathrm{min}$, which corresponds to the angular extent of the loops at the time of recombination. This results in a peak in the birefringence power spectrum around $\ell_p \sim 1/\theta_\mathrm{min}$. An additional scale, controlled by the axion's mass, is introduced if the network collapses before today.