Study the nature of dynamical dark energy by measuring the CMB polarization rotation angle

Recent results from the Dark Energy Spectroscopic Instrument (DESI) support the dynamical dark energy. Intriguingly, the data favor a transition of the dark energy equation of state across $w=-1$, a hallmark of the Quintom scenario. In this paper, we consider a different approach to the dynamical nature of dark energy by investigating its interaction with ordinary matters, specifically the Chern-Simons (CS) interaction with photons. In cosmology, this interaction rotates the polarized plane of the cosmic microwave background (CMB) photons, which induces non-zero polarized TB and EB power spectra. We forecast this measurement with the Ali CMB Polarization Telescope (AliCPT) experiment. We take the best-fit value of the isotropic rotation angle from Planck data as our fiducial input. We project that 11 module-year (modyr) of observations will yield an improved detection sensitivity with a significance $\sim 5\sigma$, given a calibration precision of $0.1^\circ$ in the polarization angle. We also forecast AliCPT's sensitivity to the amplitude of a scale invariant spectrum of the anisotropic polarization rotation field. With $50$~modyr of observations, the large-aperture configuration is expected to reach $\sigma_{A_{\mathrm{CB}}}\sim10^{-2}$, offering a sixfold improvement over the small-aperture design and enabling competitive tests of spatial fluctuations in the dark energy field.