Unveiling $ν$ secrets with cosmological data: neutrino masses and mass hierarchy

TL;DR

This work uses the latest public cosmological data within a flat $Λ$CDM framework to place the strongest bounds to date on the sum of active neutrino masses $M_ν$ and to probe the neutrino mass hierarchy. Through Bayesian inference with MCMC and a rigorous Hannestad-Schwetz model comparison, the authors quantify how much current data favors the normal over the inverted ordering, finding only mild to moderate disfavoring of IH depending on dataset choices. They compare the constraining power of geometric BAO information against full-shape galaxy power spectra, concluding that BAO remains the more powerful lever for $M_ν$ bounds under present analysis techniques, largely due to non-linear modeling and bias uncertainties in $P(k)$. Extended parameter spaces (e.g., allowing $w$ or $Ω_k$ to vary) weaken bounds and erode hierarchy discrimination, highlighting the need for next-generation data with ~0.02 eV sensitivity to conclusively determine the mass ordering from cosmology. Overall, the paper establishes a robust, conservative cosmological upper limit near 0.15 eV for $M_ν$ and shows that while current data reduce the IH’s viable parameter space, definitive hierarchy resolution awaits future surveys and refined modeling.

Abstract

Using some of the latest cosmological datasets publicly available, we derive the strongest bounds in the literature on the sum of the three active neutrino masses, $M_ν$, within the assumption of a background flat $Λ$CDM cosmology. In the most conservative scheme, combining Planck cosmic microwave background (CMB) temperature anisotropies and baryon acoustic oscillations (BAO) data, as well as the up-to-date constraint on the optical depth to reionization ($τ$), the tightest $95\%$ confidence level (C.L.) upper bound we find is $M_ν<0.151$~eV. The addition of Planck high-$\ell$ polarization data, which however might still be contaminated by systematics, further tightens the bound to $M_ν<0.118$~eV. A proper model comparison treatment shows that the two aforementioned combinations disfavor the IH at $\sim 64\%$~C.L. and $\sim 71\%$~C.L. respectively. In addition, we compare the constraining power of measurements of the full-shape galaxy power spectrum versus the BAO signature, from the BOSS survey. Even though the latest BOSS full shape measurements cover a larger volume and benefit from smaller error bars compared to previous similar measurements, the analysis method commonly adopted results in their constraining power still being less powerful than that of the extracted BAO signal. Our work uses only cosmological data; imposing the constraint $M_ν>0.06\,{\rm eV}$ from oscillations data would raise the quoted upper bounds by ${\cal O}(0.1σ)$ and would not affect our conclusions.

Figures (7)

• Figure 1: Top: Non-linear galaxy power spectrum computed using the Halofit method with the camb code Lewis:1999bs (red line) and the Coyote emulator (blue line) Heitmann:2008eqHeitmann:2013braKwan:2013jva at z=0.57 for the $\Lambda$CDM best-fit parameters from Planck TT 2015 data and $M_{\nu}=0\,{\rm eV}$ (given that the emulator does not fully implement corrections due to non-zero neutrino masses on small scales). Green triangle data points are the clustering measurements from the BOSS DR12 CMASS sample. The error bars are computed from the diagonal elements $C_{ii}$ of the covariance matrix. For comparison with previous work Giusarma:2016phn, purple circles represent clustering measurements from the BOSS Data Release 9 (DR9) CMASS sample. A very slight suppression in power on small scales (large $k$) of the DR12 sample compared to the DR9 sample is visible. Note that the binning strategy adopted in DR9 and DR12 is different. Bottom: Residuals with respect to the non-linear model with Halofit. The orange horizontal line indicates the $k$ range used in our analysis. As it is visually clear, the $k$ range we choose is safe from large non-linear corrections.
• Figure 2: Posteriors of $M_\nu$ obtained with baseline datasets basePK and baseBAO, in combination with additional external datasets. This allows for a comparison of the constraining power of shape information in the form of the full shape galaxy power spectrum, and geometrical information in the form of BAO measurements, when CMB full temperature and low-$\ell$ polarization data are used. To compare the relative constraining power of shape and geometrical information, compare the solid and dashed lines for a given color: red (basePK against baseBAO), blue (basePK+$\tau0p055$ against baseBAO+$\tau0p055$), and black (basePK+$H073p02+\tau0p055$ against baseBAO+$H073p02+\tau0p055$). The dotted line at $M_\nu=0.0986$ eV denotes the minimal allowed mass in the IH scenario. It can be clearly seen that with our current analyses methods geometrical information supersedes shape information in constraining power.
• Figure 3: As Fig. \ref{['fig:shape_vs_geometry_planck']}, but with the addition of high-$\ell$ polarization anisotropy data. Hence, the datasets considered are the baseline datasets basePK and baseBAO, and combinations with external datasets. Once more, it can be clearly seen that with our current analyses methods geometrical information supersedes shape information in constraining power.
• Figure 4: $68\%$ C.L. (dark blue) and $95\%$ C.L. (light blue) joint posterior distributions in the $M_{\nu}$-$w$ plane, along with their marginalized posterior distributions, for the baseBAO data combination (see the caption of Tab. \ref{['tab:tabmnubao']} for further details). Ticks on the $w$-axis of the upper left plot are the same as those for the lower left plot.
• Figure 5: $68\%$ C.L. (dark blue) and $95\%$ C.L. (light blue) joint posterior distributions in the $M_{\nu}$-$\Omega_k$ plane, along with their marginalized posterior distributions, for the baseBAO data combination (see the caption of Tab. \ref{['tab:tabmnubao']} for further details). Ticks on the $\Omega_k$-axis of the upper left plot are the same as those for the lower left plot.