A short blanket for cosmology: the CMB lensing anomaly behind the preference for a negative neutrino mass

TL;DR

This work investigates why analyses combining CMB and BAO data sometimes prefer a negative effective neutrino mass. By introducing $\sum \tilde{m}_\nu$ (allowed to be negative) and a two-parameter lensing decomposition $A^{\mathrm{TTTEEE}}_{lens}$ and $A^{\phi\phi}_{lens}$, the authors explore degeneracies between neutrino mass and lensing effects using Planck, ACT lensing, DESI BAO, and a refined CMB likelihood (SRoll2/HiLLiPoP). They find the negative-mass tendency is primarily driven by an excess lensing amplitude $A^{\phi\phi}_{lens}$ detected by late-time probes relative to Planck, and that allowing both lensing amplitudes to vary brings the inferred $\sum \tilde{m}_\nu$ into closer agreement with the normal-order minimum, though a residual lensing anomaly remains. The results illustrate a broad tension between early- and late-time cosmological measurements and show that breaking degeneracies with additional probes is essential for a robust determination of the absolute neutrino mass scale; future large-scale structure data will be crucial for a definitive resolution. The study also highlights how refined likelihoods can mitigate, but not completely remove, this multi-probe tension.

Abstract

Recent analyses combining cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) challenge particle physics constraints on the total neutrino mass, pointing to values smaller than the lower limit from neutrino oscillation experiments. To examine the impact of different CMB likelihoods from $\mathit{Planck}$, lensing potential measurements from $\mathit{Planck}$ and ACT, and BAO data from DESI, we introduce an effective neutrino mass parameter ($\sum \tilde{m}_ν$) which is allowed to take negative values. We investigate its correlation with two extra parameters capturing the impact of gravitational lensing on the CMB: one controlling the smoothing of the peaks of the temperature and polarization power spectra; one rescaling the lensing potential amplitude. In this configuration, we infer $\sum \tilde{m}_ν=-0.018^{+0.085}_{-0.089}~\text{eV}~(68\% ~\text{C.L.})$, which is fully consistent with the minimal value required by neutrino oscillation experiments. We attribute the apparent preference for negative neutrino masses to an excess of gravitational lensing detected by late-time cosmological probes compared to that inferred from $\mathit{Planck}$ CMB angular power spectra. We discuss implications in light of the DESI BAO measurements and the CMB lensing anomaly.

Figures (11)

• Figure 1: 1D marginalized posterior distribution for $\sum \tilde{m}_\nu$, $n_s$, $A^{\mathrm{TTTEEE}}_\text{lens}$ an $A^{\phi\phi}_\text{lens}$. All analyses include P-ACT lensing, low-$\ell$ TT data from Commander, low-$\ell$ EE data from SRoll2, and high-$\ell$ TTTEEE data from HiLLiPoP. Lensing amplitude parameters are varied in all cases. Orange curves include DESI DR2 BAO; blue exclude it. Dashed lines indicate the scenario with fixed neutrino mass, $\sum m_\nu = 0.06~\mathrm{eV}$, while solid lines represent cases where it is allowed to vary freely. Vertical dashed lines mark the NO mass limit and the fiducial lensing values. The grey shaded region indicates the unphysical parameter space.
• Figure 2: Constraints for $A_s$, $\sum \tilde{m}_\nu$, $n_s$ and $A^{\phi\phi}_\text{lens}$. All analyses include the base data sets (DESI DR2 BAO, P-ACT lensing, low-$\ell$ TT from Commander) with the addition of SRoll2 and HiLLiPoP. Solid lines denote cases with free neutrino mass, while dashed lines keep the mass fixed to $\sum m_\nu = 0.06~\mathrm{eV}$. Filled contours indicate that the lensing amplitude parameters are varied, empty contours correspond to analyses where they are held fixed. Vertical grey dashed lines mark the NO mass limit and the fiducial value of unity for the lensing amplitude parameters. The grey shaded region indicates the unphysical parameter space.
• Figure 3: Constraints on $\sum \tilde{m}_\nu$, $A^{\phi\phi}_\text{lens}$ and $A^{\mathrm{TTTEEE}}_\text{lens}$. All analyses include the base data sets (DESI DR2 BAO, P-ACT lensing, low-$\ell$ TT from Commander), with the addition of SRoll2 and HiLLiPoP. The neutrino mass is allowed to vary. Orange contours correspond to the case where both lensing amplitude parameters are varied, blue contours to the case with $A^{\mathrm{TTTEEE}}_\text{lens}=1$, and green contours to the case with $A^{\phi\phi}_\text{lens}=1$. The grey shaded region indicates the unphysical parameter space.
• Figure 4: 1D marginalized posterior distribution for $\sum \tilde{m}_\nu$, $n_s$$\Omega_\mathrm{m}$ and $A^{\phi\phi}_\text{lens}$. All analyses include the base data sets (DESI DR2 BAO, P-ACT lensing, low-$\ell$ TT from Commander) with the addition of SRoll2 and HiLLiPoP. The green line shows the posterior distribution for the case where only the neutrino mass is varied in addition to the $\Lambda$CDM parameters. The orange line corresponds to the case in which both $\sum \tilde{m}_\nu$ and $A^{\phi\phi}_\text{lens}$ are treated as free parameters, while the blue line depicts the case in which $A^{\phi\phi}_\text{lens}$ is varied but the neutrino mass is fixed to the NO limit. Vertical grey dashed lines mark the NO mass limit and the fiducial value of unity for the lensing anomaly parameter. The grey shaded region indicates the unphysical parameter space.
• Figure 5: Left: Best-fit reconstruction of the isotropic BAO distance, normalized by its value in $\Lambda$CDM. The purple points correspond to the DESI DR2 BAO measurements reported in Table IV of DESI:2025zgx. All analyses include P-ACT lensing, low-$\ell$ TT data from Commander, low-$\ell$ EE data from SRoll2, and high-$\ell$ TTTEEE data from HiLLiPoP. Solid lines include BAO data from DESI DR2, while dashed lines exclude this data set and fix the neutrino mass to the NO lower limit. Orange curves correspond to analyses with varying lensing amplitude parameters; green curves represent cases where these parameters are fixed. The brown dashed line and shaded region represents the mean and $68\%$ C.L. of the baseline BAO+CMB result from DESI:2025ejh, where the CMB data set corresponds to the combination base + SimAll + CamSpec. This configuration yields a value of $\sum m_\nu = -0.101~\mathrm{eV}$. Right: 1D posterior distribution of $H_\mathrm{0}r_d$ for the same configurations shown in the left panel. The vertical shaded bands indicate the 68$\%$ and 95$\%$ confidence regions from the DESI DR2 BAO data.