Conversations in the dark: cross-correlating birefringence and LSS to constrain axions

Unveiling the dark sector of the Universe is one of the leading efforts in theoretical physics. Among the many models proposed, axions and axion-like particles stand out due to their solid theoretical foundation, capacity to contribute significantly to both dark matter and dark energy, and potential to address the small-scale crisis of ΛCDM. Moreover, these pseudo-scalar fields couple to the electromagnetic sector through a Chern-Simons parity-violating term, leading to a rotation of the plane of linearly polarized waves, namely cosmic birefringence. We explore the impact of the axion-parameters on anisotropic birefringence and study, for the first time, its cross-correlation with the spatial distribution of galaxies, focusing on ultralight axions with masses 10-33 eV ≤ mϕ ≤ 10-28 eV. Through this novel approach, we investigate the axion-parameter space in the mass mϕ and initial misalignment angle θi, within the framework of early dark energy models, and constrain the axion-photon coupling gϕγ required to achieve unity in the signal-to-noise ratio of the underlying cross-correlation, computed with the instrument specifications of Euclid and forthcoming CMB-polarization data. Our findings reveal that for masses below 10-32 eV and initial misalignment angles greater in absolute value than π/4, the signal-to-noise ratio not only exceeds unity but also surpasses that achievable from the auto-correlation of birefringence alone (up to a factor 7), highlighting the informative potential of this new probe. Additionally, given the late-time evolution of these low-mass axions, the signal stems from the epoch of reionization, providing an excellent tool to single out the birefringence generated during this period.