Neutrino mass limits: robust information from the power spectrum of galaxy surveys

TL;DR

This work derives cosmological upper limits on the sum of active neutrino masses $M_\nu$ by combining Planck 2015 CMB data with full-shape galaxy power spectra from two tracers: SDSS-DR7 LRG and WiggleZ. It demonstrates robustness against galaxy bias by showing consistent constraints from these distinct tracers and highlights the critical role of BAO measurements in breaking degeneracies, achieving $M_\nu<0.13$ eV (LRG) and $M_\nu<0.14$ eV (WiggleZ) at 95% C.L. when BAO is included, with slightly weaker bounds without BAO or when lensing is included. The results are competitive with the strongest existing limits (e.g., Ly$\alpha$-based) and favor the normal neutrino mass hierarchy, underscoring the power of full-shape large-scale structure data for neutrino physics. Overall, the paper reinforces the robustness of cosmological neutrino mass inferences across independent galaxy tracers and demonstrates the strong constraining power of combining CMB, BAO, and galaxy power spectra.

Abstract

We present cosmological upper limits on the sum of active neutrino masses using large-scale power spectrum data from the WiggleZ Dark Energy Survey and from the Sloan Digital Sky Survey - Data Release 7 (SDSS-DR7) sample of Luminous Red Galaxies (LRG). Combining measurements on the Cosmic Microwave Background temperature and polarisation anisotropies by the Planck satellite together with WiggleZ power spectrum results in a neutrino mass bound of 0.37 eV at 95% C.L., while replacing WiggleZ by the SDSS-DR7 LRG power spectrum, the 95% C.L. bound on the sum of neutrino masses is 0.38 eV. Adding Baryon Acoustic Oscillation (BAO) distance scale measurements, the neutrino mass upper limits greatly improve, since BAO data break degeneracies in parameter space. Within a $Λ$CDM model, we find an upper limit of 0.13 eV (0.14 eV) at 95% C.L., when using SDSS-DR7 LRG (WiggleZ) together with BAO and Planck. The addition of BAO data makes the neutrino mass upper limit robust, showing only a weak dependence on the power spectrum used. We also quantify the dependence of neutrino mass limit reported here on the CMB lensing information. The tighter upper limit (0.13 eV) obtained with SDSS-DR7 LRG is very close to that recently obtained using Lyman-alpha clustering data, yet uses a completely different probe and redshift range, further supporting the robustness of the constraint. This constraint puts under some pressure the inverted mass hierarchy and favours the normal hierarchy.

Figures (9)

• Figure 1: Effect (absolute on the left panel and relative to the massless neutrino case on the right panel) of neutrino mass on the non-linear matter power spectrum at $z=0$ for the $k$-range used in this analysis, prior to applying the window function of the survey. Shown are the power spectrum for massless neutrinos (blue), for the neutrino mass close to the CMB+BAO+$P(k)$ bound in this paper (green), and for the neutrino mass close to the bound given by current CMB+$P(k)$ data (red) while $\Omega_m$, and all other cosmological parameters (except for $\omega_{\rm{cdm}}$) are kept fixed. The dashed red line is the red line renormalised (akin to a scale-independent bias factor) to match the blue one at $k=0.05$$h$ Mpc$^{-1}$.
• Figure 2: LRG and WZ data sets used. The LRG data are at $z\sim 0.35$ (but normalised to $z=0$) and WZ is separated in four redshift bins at effective redshifts $z=0.22, 0.41, 0.6, 0.78$, only band powers with $k<0.2$$h$ Mpc$^{-1}$ are used here. A visual comparison of the two data sets might be misleading since not only the galaxy samples but also the window functions of the two surveys are different.
• Figure 3: LRG (left) and WZ (right) data sets used and the theoretical best-fit obtained from CMB+$P(k)$ data (solid line). The dashed line corresponds to a model with $M_{\nu}$ corresponding to the 95% limit for CMB data, keeping all other parameters fixed except for $\omega_{\rm{cdm}}$. The WZ plot is normalised so that all the lines overlap at large scales. In the upper (lower) panels we show the non-linear matter power spectrum after (before) applying the window function of the two surveys. As opposed to Fig. \ref{['fig:pk_mnu']}, here the theory power spectrum is multiplied by the marginalised value of the square of the galaxy bias for each model.
• Figure 4: Comparison between the posterior distribution of the sum of neutrino masses, $M_\nu$, from the following data combinations: CMB15 + LRG (+lensing) and CMB15 + LRG + BAO (+lensing), in the left panel; CMB15 + WiggleZ (+lensing) and CMB15 + WiggleZ + BAO (+lensing), in the right panel. CMB15 indicates the 2015 Planck TT,TE,EE + lowP data. For a detailed description of the individual data sets used, we refer to Sec. \ref{['sec:data']}. We use black (blue dashed) lines when power spectrum data are combined with CMB15 (+lensing) data and red (yellow dashed) lines when also BAO is added.
• Figure 5: Two-dimensional posterior distribution for ($\tau_{\rm{reio}}, M_\nu, H_0, \sigma_8$) parameters from the CMB15 + LRG + BAO (red contours) and CMB15 + WZ + BAO (blue contours) data sets. The $1~\sigma$ and $2~\sigma$ contours are shown.