CMB birefringence from ultralight-axion string networks

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 structure network. We develop an approximate analytic formalism identify a kernel function that be used to calculate two-point correlation for CMB induced by arbitrary Using formalism, we evaluate signal some simple loop distributions (including scaling network collapse). find angular has characteristic scale set $\theta_\mathrm{min}$, which corresponds extent loops at time recombination. This results in peak power spectrum around $\ell_p \sim 1/\theta_\mathrm{min}$. An additional scale, controlled axion's mass, introduced if collapses before today.