Resolving the negative effective neutrino mass parameter with cosmic birefringence

Abstract

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 $Λ$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 $Λ$CDM by assuming a higher optical depth ($τ\simeq 0.09$), 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 $β_0=0.34\pm0.09\,(1\,σ)\,$deg has the phase ambiguity, i.e., the measured rotation angle is described by $β=β_0+180n\,$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 $τ$ 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 $τ$, suggesting a key role for cosmic birefringence in current cosmological tensions.

Figures (2)

• Figure 1: Likelihood bound on the ALP logarithmic mass, $\mu = \log_{10}(m_\phi, [{\rm eV}])$, and the optical depth, $\tau$, for a fixed value of $n = 1$ (left) and $n=2$ (right). We plot the log-likelihood difference with the $2\,\sigma$ confidence region (the black contour) that corresponds to $\lambda\equiv-\ln\mC{L}/\mC{L}_{\rm max}=3.0$. The constraints are obtained using the low-$\ell$$EE + EB + BB$. The black stars are the maximum likelihood (ML) points. $\chi^2_{\rm ML}/{\rm d.o.f.}$ is the $\chi^2$ value at the ML points divided by the degree of freedom. The top gray bands, enclosed by black dashed lines, indicate the marginalized $2\,\sigma$ constraints on $\tau$ from Ref. Sailer:2025:tau derived without low-$\ell$ CMB data. The bottom thin black dashed line with the orange hatched region corresponds to the $2\,\sigma$ constraint on $\tau$ from Planck PR4 Tristram:2023:PR4:cosmo.
• Figure 2: Angular power spectra of $EE$ (top left), $EB$ (top right), $BB$ (bottom left), and $TE$ (bottom right) for selected values of $\mu$, $\tau$, and $n$ that provide a good fit to both the low-$\ell$ polarization data and the optical depth constraint $\tau = 0.095 \pm 0.014$ (1$\sigma$). The black solid and dashed curves correspond to the theoretical spectra for $n=0$ with $\tau=0.095$ obtained without the low-$\l$ CMB data Sailer:2025:tau and with $\tau=0.058$ obtained from the Planck PR4 analysis Tristram:2023:PR4:cosmo, respectively. In these two curves, we fix $\mu=-31$ but the dependence of the spectra shown here on $\mu$ is negligible in the figures. The vertical axis shows $D_\l = \l(\l+1)C_\l/(2\pi)$. Observational data points for $EE$, $EB$, and $BB$ are taken from the Planck PR4 release Tristram:2020:PR4:r, while $TE$ data points are from Planck PR3 PR3:Cl.