Redshift evolution of cosmic birefringence in CMB anisotropies

We study the imprints of a cosmological redshift-dependent pseudoscalar field phi on the rotation of cosmic microwave background (CMB) linear polarization generated by a coupling phi F mu nu F similar to mu nu. We show how either phenomenological or theoretically motivated redshift dependence of the pseudoscalar field, such as those in models of early dark energy, quintessence, or axionlike dark matter, lead to CMB polarization and temperature-polarization power spectra which exhibit a multipole dependence which goes beyond the widely adopted approximation in which the redshift dependence of the linear polarization angle is neglected. Because of this multipole dependence, the isotropic birefringence effect due to a general coupling phi F mu nu F similar to mu nu is not degenerate with a systematic calibration angle uncertainty. By taking this multipole dependence into account, we calculate the parameters of these phenomenological and theoretical redshift dependencies of the pseudoscalar field which can be detected by future CMB polarization experiments on the basis of a chi 2 analysis for a Wishart likelihood. As a final example of our approach, we compute by Markov chain Monte Carlo the minimal coupling g phi in early dark energy which could be detected by future experiments, with or without marginalizing on a systematic rotation angle uncertainty.

Automated summary

We study the impact of a cosmological redshift-dependent pseudoscalar field on the rotation of cosmic microwave background linear polarization. It is found that the redshift dependence leads to multipole dependence in the polarization and temperature-polarization power spectra. Taking this into account, we calculate the parameters of the redshift dependencies that can be detected by future CMB polarization experiments.