REVIEW
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
Cosmology and Nongalactic Astrophysics · Submitted 15 Nov 2012 · 120 references
Pith's verdict: A solid, well-bookkept neutrino-mass measurement from CMASS DR9 whose flat-LCDM 0.340 eV bound holds up; the all-float branch has three internal number conflicts that need an erratum, not a rejection.
T0 · AI review
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Referee report
The paper
The paper claims
The shape of galaxy clustering puts a ceiling on neutrino mass: below 0.34 eV in a flat Lambda CDM universe, and below 0.82 eV once dark energy, curvature, running and extra species are all allowed to float.
The reading
What carries the argument
The load-bearing object is the one-loop perturbation-theory galaxy power spectrum with a massive-neutrino component, $P^{1loop}_{cbnu}(k) = f_{cb}^2 P^{1loop}_{cb}(k) + 2 f_{cb} f_{nu} P^{L}_{cbnu}(k) + f_{nu}^2 P^{L}_{nu}(k)$, where $f_{nu} = sum m_{nu} / (94.1 , mathrm{eV} cdot Omega_m h^2)$ is the neutrino fraction of the total matter density and the neutrino component is assumed to stay linear. This is promoted to a galaxy spectrum by $P_g(k;z) = b_1^2 [P^{1loop}_{cbnu} + b_2 P_{b2} + b_2^2 P_{b22}] + N$, with linear bias $b_1$, nonlinear bias $b_2$ and residual shot noise $N$ marginalised as free nuisance parameters. The theory spectrum is convolved with a window matrix extracted from the survey geometry and compared bin-by-bin to the measurement, with the covariance and window both derived from 600 two-dimensional Lagrangian perturbation theory mock catalogues. A nuisance parameter $S$ with a Gaussian prior of width $0.1$ absorbs residual uncertainty in the stellar-density weighting of the target sample. A modified CAMB plus COSMO MC Markov chain explores the parameter space.
Extended reading notes
Core claim
The central claim is that the broadband shape of the CMASS power spectrum between roughly $k = 0.02$ and $0.1$ $h$ Mpc$^{-1}$ carries enough information about neutrino free-streaming to beat a BAO-only analysis by a wide margin: substituting the CMASS BAO distance measurement for the full power spectrum weakens the 95 percent limit from $0.340$ eV to $0.579$ eV. The authors show this bound is stable against the choice of galaxy bias model (one-loop standard perturbation theory with massive neutrinos, HALOFIT-$nu$, or the Cole et al. fitting formula), against four different treatments of redshift-space distortion (from linear Kaiser through a nonlinear Kaiser model with correction terms and a finger-of-God factor), against raising the fit cutoff from $k_{max} = 0.1$ to $0.2$ $h$ Mpc$^{-1}$, and against swapping SNLS3 for Union2.1 supernovae. Alongside the mass bound they measure the effective number of relativistic species as $N_{eff} = 4.308 pm 0.794$ in a $Lambda N_{eff} m_{nu}$CDM model, about $1.6sigma$ above the standard $3.046$, and find $w = -1$, $Omega_K = 0$ and $alpha_s = 0$ all consistent with the data, with $r < 0.198$ in the minimal model.
Load-bearing premise
The error bars and bin-to-bin correlations of the measured CMASS power spectrum are correctly given by the 600 mock catalogues, which were built with a fixed cosmology containing no massive neutrinos and a fixed prescription for how galaxies populate dark matter halos, and the paper does not check that covariance against the data itself.
Editorial extensions
If this is right
- A 95 percent upper limit of $0.340$ eV on the sum of neutrino masses in flat $Lambda$CDM, degrading to $0.432$ eV when constant $w$ floats, $0.491$ eV when $N_{eff}$ floats, $0.618$ eV under the CPL parametrisation, and $0.821$ eV when curvature, running and the tensor-to-scalar ratio also float.
- The broadband power spectrum shape, not the baryon acoustic wiggles, is what delivers the neutrino information: BAO alone gives $0.579$ eV, so the shape roughly halves the allowed mass range.
- The effective number of relativistic species comes out at $4.308 pm 0.794$, leaving room for roughly one extra light species beyond the standard three, in line with similar excesses reported by other CMB experiments.
- The dark energy equation of state, spatial curvature and running of the spectral index all remain consistent with their standard values even after neutrino mass is marginalised over, and $r < 0.198$ at 95 percent confidence in the minimal model.
- Freeing the neutrino mass degrades the measurement of $Omega_M$ and $H_0$ by only about ten percent, but freeing the full parameter set degrades them substantially, to $Omega_M = 0.2798$ and $H_0 = 73.78$ km/s/Mpc with errors several times larger.
Reading between the lines
- The quoted bound sits well above the roughly $0.06$ eV floor implied by neutrino oscillation data for normal ordering, so this measurement cannot yet discriminate mass ordering; the same shape-based technique applied to a larger volume is the natural route toward that floor.
- The measured $N_{eff}$ excess of about $1.6sigma$ is degenerate with the physical matter density $Omega_M h^2$ by construction, so an independent, tighter determination of the matter density would either confirm an extra relativistic species or pull the preferred $N_{eff}$ back toward $3.046$.
- The orderly degradation of the bound, from $0.34$ eV to $0.82$ eV as cosmological freedom is added, suggests that future galaxy-survey neutrino limits will be set less by raw clustering precision than by external priors on dark energy dynamics and curvature.
- Because the neutrino signature here is a smooth suppression of power, any unmodelled scale-dependent bias at the percent level over $0.02 < k < 0.1$ $h$ Mpc$^{-1}$ would mimic part of the effect; cross-checking the same measurement against a probe with entirely different systematics, such as the Lyman-alpha forest flux power spectrum, would test whether the suppression is genuinely neutrino free-s
Original 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 $\Sigma m_{\nu}<0.340$ eV within a flat $\Lambda$CDM background, and $\Sigma m_{\nu}<0.821$ 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 $\Omega_M=0.2796\pm0.0097$, $H_0=69.72^{+0.90}_{-0.91}$ km/s/Mpc (flat $\Lambda$CDM) and $\Omega_M=0.2798^{+0.0132}_{-0.0136}$, $H_0=73.78^{+3.16}_{-3.17}$ 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 \Omega_K and the running of the spectral index $\alpha_s$ are both consistent with zero. The tensor-to-scaler ratio is constrained down to $r<0.198$ (95 percent CL, flat $\Lambda$ CDM) and $r<0.440$ (95 percent CL, more general background model).
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
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 $\Sigma m_{\nu}<0.340$ eV within a flat $\Lambda$CDM background, and $\Sigma m_{\nu}<0.821$ 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 $\Omega_M=0.2796\pm0.0097$, $H_0=69.72^{+0.90}_{-0.91}$ km/s/Mpc (flat $\Lambda$CDM) and $\Omega_M=0.2798^{+0.0132}_{-0.0136}$, $H_0=73.78^{+3.16}_{-3.17}$ 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 \Omega_K and the running of the spectral index $\alpha_s$ are both consistent with zero. The tensor-to-scaler ratio is constrained down to $r<0.198$ (95 percent CL, flat $\Lambda$ CDM) and $r<0.440$ (95 percent CL, more general background model).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.87 | 0.97 | 0.10 | asserted 1.00 |
| s1 | 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 $\Sigma m_{\nu}<0.340$ eV within a flat $\Lambda$CDM background, and $\Sigma m_{\nu}<0.821$ eV, assuming a more general background cosmological model. | result 1.00 | 0.96 | 0.80 | asserted 1.00 |
| s2 | 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. | result 1.00 | 0.96 | 0.07 | asserted 1.00 |
| s3 | 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. | contribution 0.59 | 0.95 | 0.02 | asserted 0.97 |
| s4 | The impact of neutrinos with unknown masses on other cosmological parameter measurements is investigated. | contribution 0.97 | 0.91 | 0.02 | asserted 0.68 |
| s5 | The fractional matter density and the Hubble parameter are measured to be $\Omega_M=0.2796\pm0.0097$, $H_0=69.72^{+0.90}_{-0.91}$ km/s/Mpc (flat $\Lambda$CDM) and $\Omega_M=0.2798^{+0.0132}_{-0.0136}$, $H_0=73.78^{+3.16}_{-3.17}$ km/s/Mpc (more general background model). | result 1.00 | 0.96 | 0.06 | asserted 1.00 |
| s6 | 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. | result 1.00 | 0.97 | 0.07 | hedged possibility 0.89 |
| s7 | Similarly, the curvature \Omega_K and the running of the spectral index $\alpha_s$ are both consistent with zero. | result 0.99 | 0.92 | 0.03 | hedged possibility 0.79 |
| s8 | The tensor-to-scaler ratio is constrained down to $r<0.198$ (95 percent CL, flat $\Lambda$ CDM) and $r<0.440$ (95 percent CL, more general background model). | result 1.00 | 0.95 | 0.05 | asserted 1.00 |
What was examined, and what was not
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Figures
Showing 15 of the paper's 19 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:1211.3741 by the authors.
References
How later papers used it
55 later papers cite it
1 later paper by other authors is listed below: 1 used its data or values.
Uses its data or values 1 of 4 papers with this label
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Adopted this paper's constraint of Σmν ≤ 0.34 eV (95% CL) in the flat ΛCDM model to ignore neutrino mass uncertainty when constraining δg.
Measuring Speed of Gravitational Waves by Observations of Photons and Neutrinos from Compact Binary Mergers and Supernovae (2014) · 0.95 · paraphrased: the licence does not allow quoting
How the literature uses it
46 arXiv papers cite this in 58 sentences
Papers citing it · 38 sentences without a confident label
Uses its method or tool 1 paper
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We model the galaxy bias and the redshift space distortion using the approach developed in [ref] and applied to CMASS in [ref] .
Reconstructing primordial power spectrum using Planck and SDSS-III measurements · Introduction · 0.97
Uses its data or values 4 papers
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Together with Planck CMB temperature and polarization measurements, we exploit here the DR9 CMASS sample of galaxies [ref] , as previously done in Refs. [ref] .
On the improvement of cosmological neutrino mass bounds · Analysis and data · 0.91
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The curvature parameter has also been measured by galaxy surveys such as BOSS, which arrived at $Ω_K =-0.00264^+0.00466_-0.00461$, or $Ω_K = -0.00411 ±0.01029$ with more conservative assumptions [ref] , and with a more recent analysis $Ω_K = 0.0010±0.0029$ [ref] ; WiggleZ found $Ω_K = -0.0043 ±0.0047$ [ref] .
Curvature constraints from Large Scale Structure · Introduction · 0.82
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Recent constraints on the upper limit of the total neutrino mass lie in the range $∑m_ν< 0.3 - 0.8 eV$ ($95%$ Confidence Level (CL)) [ref] , with notable exception of Lyman$-α$ data, which presents an even tighter bound of $0.17 eV$ [ref] .
Constraining neutrino properties with a Euclid-like galaxy cluster survey · Introduction · 0.81
Compares with it 3 papers
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In table [ref] we show the constraint on the total neutrino mass from all datasets together, namely the $95%$ upper limit is $∑m_ν<0.47$eV, which is consistent with previous works [ref] .
Constraints on Scalar Spectral Index from Latest Observational Measurements · Neutrino Properties · 0.97
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* From the combination of Euclid number counts and clustering data we obtain a $2σ$ upper limits for the total neutrino mass of $∑m_ν<0.35 eV$, comparable with present constraints from the combination of CMB and LSS probes [ref] .
Constraining neutrino properties with a Euclid-like galaxy cluster survey · Conclusions · 0.99
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The two most relevant constraints with spectroscopic galaxy samples are those from the WiggleZ [ref] and BOSS experiments [ref] , both of which find $∑m_ν≤0.34$ at the 95% CL.
Cluster Cosmology at a Crossroads: Neutrino Masses · The Role of External Data · 0.84
Cites it as background 11 papers
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This has been explored in various papers (e.g. [ref] ).
Exploring Early and Late Cosmology with Next Generation Surveys · Introduction · 0.87
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Current cosmological evidence for extra neutrinos from CMB and large-scale structure observations is discussed in Refs. [ref] ; however, see Refs. [ref] for a different interpretation.
Is there evidence for additional neutrino species from cosmology? · Introduction · 0.80
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The effects on cosmological parameter estimation of considering a PPS which is different from a power-law has been studied in several works: for example, the power-law PPS has been simply modified with the introduction of a running in the tilt of the power-law [ref] , a running of the running [ref] , or a sharp cut-off in the power-law [ref] .
Light Sterile Neutrinos and Inflationary Freedom · Introduction · 0.93
Discussion
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