The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: weighing the neutrino mass using the galaxy power spectrum of the CMASS sample

TL;DR

The study uses the SDSS-III CMASS DR9 galaxy power spectrum, in combination with CMB, SN, and BAO data, to constrain the sum of neutrino masses $Σm_{ν}$ and the effective number of neutrino species $N_{eff}$ under both a flat $Λ$CDM background and more general cosmologies. By employing perturbation theory with massive neutrinos, several RSD models, and complementary fitting formulas (HALOFIT-$ν$ and Cole 2005), the authors quantify how modeling choices affect $Σm_{ν}$ and show that broadband $P(k)$ information (including small-scale suppression) provides stronger constraints than BAO alone. They report $Σm_{ν}<0.340$ eV (95% CL) in ΛCDM and $Σm_{ν}<0.821$ eV in the most general cosmology, with $N_{eff}≈4.3$ in their baseline extensions, while allowing other parameters (e.g., $w$, $Ω_K$, $α_s$, and $r$) to float degrades neutrino bounds through degeneracies. The results favor a universe close to flat with $w≈-1$ and indicate modest evidence for $N_{eff}>3$, highlighting the continued leverage of large-scale structure data in neutrino cosmology and its interplay with dark energy and early-universe physics.

Abstract

We measure the sum of the neutrino particle masses using the three-dimensional galaxy power spectrum of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) CMASS galaxy sample. Combined with the cosmic microwave background (CMB), supernova (SN) and additional baryonic acoustic oscillation (BAO) data, we find upper 95 percent confidence limits of the neutrino mass $Σm_ν<0.340$ eV within a flat $Λ$CDM background, and $Σm_ν<0.821$ eV, assuming a more general background cosmological model. The number of neutrino species is measured to be $N_{\rm eff}=4.308\pm0.794$ and $N_{\rm eff}=4.032^{+0.870}_{-0.894}$ for these two cases respectively. We study and quantify the effect of several factors on the neutrino measurements, including the galaxy power spectrum bias model, the effect of redshift-space distortion, the cutoff scale of the power spectrum, and the choice of additional data. The impact of neutrinos with unknown masses on other cosmological parameter measurements is investigated. The fractional matter density and the Hubble parameter are measured to be $Ω_M=0.2796\pm0.0097$, $H_0=69.72^{+0.90}_{-0.91}$ km/s/Mpc (flat $Λ$CDM) and $Ω_M=0.2798^{+0.0132}_{-0.0136}$, $H_0=73.78^{+3.16}_{-3.17}$ km/s/Mpc (more general background model). Based on a Chevallier-Polarski-Linder (CPL) parametrisation of the equation-of-state $w$ of dark energy, we find that $w=-1$ is consistent with observations, even allowing for neutrinos. Similarly, the curvature Ω_K and the running of the spectral index $α_s$ are both consistent with zero. The tensor-to-scaler ratio is constrained down to $r<0.198$ (95 percent CL, flat $Λ$ CDM) and $r<0.440$ (95 percent CL, more general background model).

Figures (19)

• Figure 1: The power spectrum measured from the CMASS sample. The correlation coefficients obtained from the mock catalogues and the expected window functions are shown in the middle and bottom row. See text for more details.
• Figure 2: An example of comparison among the RSD models. Upper: the monopole power spectra for the RSD models shown in the text; RSD 1: the Linear Kaiser ( red), RSD 2: the Nonlinear Kaiser ( blue for SPT and green for CLA), RSD 3: the Nonlinear Kaiser with the FoG prefactor ( magenta), and RSD 4: the Nonlinear Kaiser plus correction terms with the FoG ( black). Each spectrum is divided by the Linear Kaiser model with linear no-wiggle spectrum for clarification purpose. We consider the cosmology for the CMASS mocks and the best-fit parameters of $(b_{1},b_{2},N)$ in the case of $\Lambda m_{\nu}$CDM model. We use the linear velocity dispersion, $\sigma_{\rm V}=4.57\,{\rm Mpc}/h$ when computing the FoG prefactor. For comparison, the Linear Kaiser models with $b_{2}=-0.2$ ( red dashed) and with $\sum m_{\nu}=0.1\,{\rm eV}$ ( red dotted) are also shown. Lower: fractional difference of each model from the RSD model 4. The line colours and styles denote exactly same with those in the upper panel. We show the error bars taken from diagonal components in the CMASS covariance matrix as a reference.
• Figure 3: The purple and green contours on the top layer in left panels: the 68 and 95 percent CL contour plots for neutrino mass and $\Omega_{\rm M}$ obtained from the joint dataset including CMB+SN+CMASS power spectra cut off at various $k$ illustrated in the figure; The blue contours on the bottom layer in left panels: the 68 and 95 percent CL contour plots for neutrino mass and $\Omega_{\rm M}$ obtained from the joint dataset including CMB+SN+CMASS BAO; Right panel: the corresponding $1D$ posterior distribution of neutrino mass. A $\Lambda$CDM model is assumed for the background cosmology.
• Figure 4: The CMASS data used in the analysis and the best fit power spectrum assuming a $\Lambda m_{\nu}$CDM cosmology. The data and spectra are both rescaled using the linear matter spectrum for the best fit model. The upper and lower panels show the cases of $k_{\rm max}=0.1$ and $0.2\,h\,{\rm Mpc}^{-1}$ respectively.
• Figure 5: The 68 and 95 percent CL contour plot for neutrino mass and $\Omega_{\rm M}$ using three different galaxy modelling.