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 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(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 l(p) similar to 1/theta(min). An additional scale, controlled by the axion's mass, is introduced if the network collapses before today.

Automated summary

Studying the birefringence of CMB photons passing through axion string loops can provide valuable information about axion-photon coupling and string network structure. The analysis reveals a characteristic angular scale set by theta(min) and a peak in the birefringence power spectrum around l(p) similar to 1/theta(min). An additional scale, controlled by the axion's mass, is introduced if the string network collapses before today.