Resolving the negative effective neutrino mass parameter with cosmic birefringence

The recent measurement of baryonic acoustic oscillations by the Dark Energy Spectroscopic Instrument reveals a mild tension with observations of the cosmic microwave background (CMB) within the standard $\Lambda$CDM cosmological model. This discrepancy leads to a preference for a total neutrino mass that is lower than the minimum value inferred from neutrino oscillation experiments. Alternatively, this tension can be eased within $\Lambda$CDM by assuming a higher optical depth ($\tau \simeq 0.09$), but such a value conflicts with large-scale CMB polarization data. We point out that cosmic birefringence, as suggested by recent Planck reanalyses, resolves this discrepancy if the birefringence angle varies significantly during reionization. Specifically, we consider the fact that the measured cosmic birefringence angle $\beta_0=0.34\pm0.09\,(1\,\sigma)\,$deg has the phase ambiguity, i.e., the measured rotation angle is described by $\beta=\beta_0+180n\,$deg ($n\in \mathbb{Z}$). We show that cosmic birefringence induced by axion-like particles with nonzero $n$ suppresses the reionization bump, allowing a higher $\tau$ consistent with data. We provide a viable parameter space where the birefringence effect simultaneously accounts for the low-$\ell$ polarization spectra, the Planck $EB$ correlations, and the elevated value of $\tau$, suggesting a key role for cosmic birefringence in current cosmological tensions.