CERN Accelerating science

Impact of a non-zero neutrino mass on the TT power spectrum. Inspired by Figure 26.2 of~\cite{Workman:2022ynf} but showing the Planck error bars taken from the binned PR3 data release\footnote{\url{https://irsa.ipac.caltech.edu/data/Planck/release_3/ancillary-data/}}. Note that it is precisely in the range of angular scales where the main impact of neutrino masses appears where the lensing anomaly is present in some Planck likelihood implementations.

Implications of BAO measurements of $\Omega_m$ and $H_0 r_d$ for $\sum m_\nu$ inferences. We show the posterior density contours using Planck data (grey and dots), as well as the regions favoured by the full SDSS BAO sample (in blue), DESI-Y1 (in red), and DESI-Y1 without the $z=0.7$ bin, which contains a $2.6\sigma$ outlier (in black dashed). We can clearly see that the $z=0.7$ leads to a relevant shift on the parameter space with implications for the neutrino mass.

Profile likelihoods for the neutrino masses within $\Lambda$CDM for three different versions of the Planck likelihoods: \texttt{Planck18-PR3}, \texttt{CamSpec22-PR4}, and \texttt{HiLLiPoP23-PR4}. For comparison purposes we also show the Planck 2013 results from~\cite{Planck:2013nga} in red where the potential trend for a best fit in the ``negative" regime was first highlighted. We clearly see that the bound on the neutrino masses changes significantly for each implementation of the likelihood, being HiLLiPoP the one giving the looser constraints. Solid and dashed lines correspond to parabolic fits where the $\Delta \chi^{2}$ points up to 4 or 2 were used in the fit, respectively.

Neutrino mass profile likelihoods using the full Planck temperature and polarization data for $\Lambda$CDM allowing to vary the unphysical $A_{\rm lens}$ parameter which is strongly correlated with $\sum m_\nu$. We can see that the bounds are significantly relaxed and comparable to the KATRIN laboratory upper limit.

Neutrino mass profile likelihoods using the full Planck temperature, polarization and lensing data for $\Lambda$CDM. This should be compared with Fig.~\ref{fig:mnu_planck_only} that does not include lensing.

Reconstructed posterior distribution of $\sum m_\nu$ in a mock analysis of \texttt{Planck18-PR3}+Lensing+BAO with three configurations: $\sum m_\nu =0,0.06,0.1$ eV. We also show the posterior reconstructed from the real data for comparison.

Profile likelihoods of the neutrino mass within $\Lambda$CDM when using Planck+BAO data comparing scenarios with DESI-Y1 (a), the full SDSS data (b), the combination of DESI-Y1+SDSS (c), and the DESI-Y1 data set but removing the ouliers at $z=0.7$ (d). We can clearly notice that systematically the HiLLiPoP23 likelihood implementation gives the weakest constraints, and that the two BAO measurements at $z = 0.7$ have a significant impact on both the bound on the neutrino mass as well as the potential preference for a negative best fit.

Neutrino mass profile likelihoods for Planck+DESI-Y1+Pantheon+ data set combinations. We show $\Lambda$CDM in black, varying the equation of state of dark energy in green, and allowing for $A_{\rm lens}$ to vary in blue. In the left panel we show the results for plik, in the middle for CamSpec, and in the right panel for Hillipop. We clearly see a similar behaviour for all of them and the potential preference for a negative best fit to dissapear when the equation of state of dark energy is allowed to vary.

Profile likelihoods for the data set combinations of Planck18-PR3+DESI-Y1 (black), HiLLiPoP23-PR4 (blue), Planck18-PR3+DESI-Y1-no07 (red), HiLLiPoP23-PR4+DESI-Y1-no07 (green), and compared with $\chi^2_{\rm eff}=-2\log \mathcal{P}$ from~\cite{Green:2024xbb} (purple) and~\cite{Elbers:2024sha} (orange), which have treatments for ``negative" neutrino masses. By comparing the black and blue curves we can clearly see that the bound on the neutrino mass gets relaxed if the HiLLiPoP likelihood (which does not contain a lensing anomaly) is used. However, it is clear from the extrapolated parabolas that there is still some preference for a negative neutrino mass. This, however, disappears when the DESI BAO data at $z =0.7$ which contains a $\sim 3\sigma$ outlier is removed (see red and green curves).

Posterior distributions for the same data set combinations as in Fig.~\ref{fig:mnu_planck_only} but analyzed within a Bayesian framework.

Posterior distributions for the same data set combinations as in Fig.~\ref{fig:mnu_planck_lensing} but analyzed within a Bayesian framework.

Posterior distributions for the same data set combinations as in Fig.~\ref{fig:planck_BAO} but analyzed within a Bayesian framework.

Posterior distributions for the same data set combinations as in Fig.~\ref{fig:planck_MAX} but analyzed within a Bayesian framework.

Comparison between our $\Delta\chi^2$ profiles and their gaussian extrapolation with the corresponding extrapolated $-2\log \mathcal{P}$ of Ref.~\cite{Allali:2024aiv} and Ref.~\cite{Elbers:2024sha}.

Correlations of $\sum m_\nu$ with $w_0$ and A$_{\text{lens}}$. The points are extracted from our profile likelihoods for the Planck+DESI-Y1+Pantheon+ combination, while the shaded regions correspond to the bayesian credible intervals at 1 and 2$\sigma$.