Kilobyte Cosmic Birefringence from ALP Domain Walls

ALP domain walls without strings may be formed in the early Universe. We point out that such ALP domain walls lead to both isotropic and anisotropic birefringence of cosmic microwave background (CMB) polarization, which reflects spatial configuration of the domain walls at the recombination. The polarization plane of the CMB photon coming from each domain is either not rotated at all or rotated by a fixed angle. For domain walls following the scaling solution, the cosmic birefringence of CMB is characterized by $2^{N}$, i.e. $N$-bit, of information with $N = {\cal O}(10^{3-4})$ being equal to the number of domains at the last scattering surface, and thus the name, $kilobyte~ cosmic~ birefringence$. The magnitude of the isotropic birefringence is consistent with the recently reported value, while the anisotropic one is determined by the structure of domains at the last scattering surface. The predicted cosmic birefringence is universal over a wide range of the ALP mass and coupling to photons. The detection of both signals will be a smoking-gun evidence for the ALP domain walls without strings.