Implications of cosmic birefringence for multi-field ALP dark matter

Abstract Cosmic birefringence, characterized by the observed rotation of the polarization plane of the cosmic microwave background (CMB) radiation, serves as a critical probe for testing theories beyond the standard cosmological scenario. Axion-like particles (ALPs), particularly as a promising subcomponent of dark matter candidates, possess unique advantages in naturally explaining such phenomena. Previous studies on the implications of cosmic birefringence for these ultralight ALP fields have focused on single-field models with conventional potentials. These models face exclusion due to the washout effect — a suppression of the CMB polarization power spectrum induced by oscillatory dynamics of the scalar field within the mass range of [10 -25 , 10 -22 ] eV. To address this limitation, we develop a more general theoretical framework incorporating two ALP fields, providing analytical approximations and numerical calculations. Our findings reveal that while the general superposition of two ALP fields with distinct masses can't relax the constraints imposed by the washout effect and remains insufficient to fully explain the observed rotation angle at a 95% confidence level. However, under specific conditions where the two fields are phase-aligned and their local amplitudes both reach the 95% upper confidence limit, the two-field framework can theoretically account for the signal within the 1σ observational uncertainty.