A tantalizing hint of isotropic cosmic birefringence has been found in the $EB$ cross-power spectrum of the cosmic microwave background (CMB) polarization data with a statistical significance of $3\sigma$. A pseudoscalar field coupled to the CMB photons via the Chern-Simons term can explain this observation. The same field may also be responsible for early dark energy (EDE), which alleviates the so-called Hubble tension. Since the EDE field evolves significantly during the recombination epoch, the conventional formula that relates $EB$ to the difference between the $E$- and $B$-mode autopower spectra is no longer valid. Solving the Boltzmann equation for polarized photons and the dynamics of the EDE field consistently, we find that currently favored parameter space of the EDE model yields a variety of shapes of the $EB$ spectrum, which can be tested by CMB experiments.

• Received 16 September 2022
• Accepted 25 January 2023

DOI:https://doi.org/10.1103/PhysRevD.107.L041302

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Published by the American Physical Society