Is cosmic birefringence due to dark energy or dark matter? A tomographic approach

A pseudoscalar "axionlike" field, $\phi$, may explain the $3\sigma$ hint of cosmic birefringence observed in the $EB$ power spectrum of the cosmic microwave background (CMB) polarization data. Is $\phi$ dark energy or dark matter? A tomographic approach can answer this question. The effective mass of dark energy field responsible for the accelerated expansion of the Universe today must be smaller than $m_\phi\simeq 10^{-33}$ eV. If $m_\phi \gtrsim 10^{-32}$ eV, $\phi$ starts evolving before the epoch of reionization and we should observe different amounts of birefringence from the $EB$ power spectrum at low ($l\lesssim 10$) and high multipoles. Such an observation, which requires a full-sky satellite mission, would rule out $\phi$ being dark energy. If $m_\phi \gtrsim 10^{-28}$ eV, $\phi$ starts oscillating during the epoch of recombination, leaving a distinct signature in the $EB$ power spectrum at high multipoles, which can be measured precisely by ground-based CMB observations. Our tomographic approach relies on the shape of the $EB$ power spectrum and is less sensitive to miscalibration of polarization angles.