Turning a negative neutrino mass into a positive optical depth

TL;DR

This paper investigates the apparent tension between DESI BAO and CMB observations within ΛCDM, which would imply unphysical negative neutrino masses if taken at face value. It demonstrates that the tension largely stems from CMB lensing calibration of the sound horizon and from the reionization optical depth τ inferred from large-scale polarization, and shows that relaxing these constraints can remove the minimal-mass neutrino tension and lessen the preference for dynamical dark energy. The authors explore multiple analysis variants, including reionization and inflation-model freedoms, showing that τ can plausibly be raised to ~0.09 under ΛCDM, or that inflationary adjustments can further ease the tension and reduce the need for beyond-ΛCDM dynamics. They highlight τ as a key lever linking CMB, BAO, and neutrino mass inferences and discuss forthcoming measurements (CLASS, LiteBIRD) and high-redshift probes to robustly test these possibilities.

Abstract

Under $Λ$CDM, recent baryon acoustic oscillation (BAO) distance measures from DESI, which favor a low matter density $Ω_m$, are in moderate $2-3σ$ tension with cosmic microwave background (CMB) observations. This tension appears alternately as a preference for the sum of neutrino masses dropping below the $\sum m_ν= 0.06$eV value required by neutrino oscillation measurements to formally negative values; a discrepant value of $Ω_m$ at 0.06eV; or preference for dynamical dark energy beyond $Λ$CDM. We show that this tension largely arises from the CMB lensing constraints on the calibration of the sound horizon for geometric measurements and relies on the measurement of the reionization optical depth $τ$ from large-angle CMB polarization to set the lensing amplitude. Dropping these constraints removes the neutrino tension at $\sum m_ν=0.06$eV entirely, favoring $τ= 0.091\pm 0.011$ in $Λ$CDM. Beyond $Λ$CDM, it brings the preference for $w_0-w_a$ dynamical dark energy to below $95\%$ CL. We explore the freedom in interpreting the low-$\ell$ EE polarization constraint due to analysis choices and reionization modeling beyond the standard step-function assumption and find that this drops the neutrino tension in $Λ$CDM to below $95\%$ CL. Alternately, this raising of $τ$ can also be achieved by the same reduction in large-scale curvature fluctuations that also ameliorates the low-$\ell$ temperature anomaly.

Figures (12)

• Figure 1: $M_\nu-\Omega_m$ posterior constraints for CMB and CMB + BAO datasets. Along the CMB degeneracy of $\Delta M_\nu \approx 2.5 \Delta \Omega_m/\Omega_m$ , the BAO data favor $M_\nu$ to be below the minimal values of $0.06$ and $0.1$ for normal and inverted ordering respectively (vertical dashed lines).
• Figure 2: Likelihood profiles shown as $\Delta\chi^2$ along $M_\nu$ for CMB + BAO and CMB (no low-$\ell$ EE)+BAO datasets with the zero point defined by the CMB + BAO $M_\nu=0.06$ model in Tab. \ref{['tab:chi2']} (horizontal dashed line). While CMB + BAO are in tension with both the normal and inverted-ordering minimal masses (vertical dashed lines), removing the optical depth $\tau$ information from low-$\ell$ EE restores consistency with both. Shaded bands represent a range of quadratic fits to extrapolate the profile to $M_\nu<0$ (see text).
• Figure 3: $\Lambda$CDM geometric tension in $\Omega_m-H_0$ at the minimal $M_\nu=0.06$. With neutrino masses fixed, the CMB geometric degeneracy is $\Delta\Omega_m/\Omega_m \approx -3 \Delta H_0/H_0$ and tension between $\Omega_m$ values with CMB and CMB + BAO reflect the calibration of the sound horizon in the former.
• Figure 4: CMB + BAO tension with minimal neutrino mass from normal and inverted orderings (vertical lines) is relaxed by either rescaling lensing with $A_L$ or by removing the low-$\ell$ EE constraint on $\tau$ due to the degeneracy $\Delta M_\nu \approx 5\Delta \tau \approx 2.5\Delta \ln A_L$.
• Figure 5: Posterior constraints on lensing-rescaling parameter $A_L$ with CMB and CMB + BAO. With the addition of BAO, $A_L$ becomes strongly inconsistent with the $\Lambda$CDM value of $A_L=1$, with a maximum likelihood value of $A_L=1.09$.