Exact CMB B-mode power spectrum from anisotropic cosmic birefringence

TL;DR

This paper calculates the CMB B-mode power spectrum caused by anisotropic cosmic birefringence without the thin approximation, revealing significant amplitude suppression and constraining the birefringence amplitude using observational data.

Contribution

It provides the first exact calculation of the CMB B-mode spectrum from anisotropic birefringence, improving upon previous thin approximation methods.

Findings

Amplitude suppression of B-mode spectrum at large scales by an order of magnitude

Amplitude reduction at small scales by a factor of two

Constraint on birefringence amplitude from SPTpol data

Abstract

We calculate the cosmic microwave background (CMB) $B$-mode power spectrum resulting from anisotropic cosmic birefringence, without relying on the thin approximation of the last scattering surface. Specifically, we consider the influence of anisotropic cosmic birefringence arising from massless axion-like particles. Comparing our results to those obtained using the thin approximation, we observe a suppression in the amplitude of the $B$-mode power spectrum by approximately an order of magnitude at large angular scales ($\ell \lesssim 10$) and by a factor of two at small angular scales ($\ell \gtrsim 100$) when not employing the thin approximation. We also constrain the amplitude of the angular power spectrum of the scale-invariant anisotropic cosmic birefringence using the SPTpol $B$-mode power spectrum. We find that the amplitude is constrained as $A_{\rm CB}\times10^4=1.03^{+0.91}_{-0.97}\,(2\,\sigma)$. The numerical code is publicly available at https://github.com/toshiyan/biref-aniso-bb/tree/main.