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Observational constraints on cosmic neutrinos and dark energy revisited
Cosmology and Nongalactic Astrophysics · Submitted 8 Oct 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The best-fit values from our most generalized constraint read $\mnu=0.556^{+0.231}_{-0.288}\rm eV$, $\neff=3.839\pm0.452$, and $w=-1.058\pm0.088$ at 68% confidence level, which shows a firm lower limit on total neutrino mass, favors an extra light degree of freedom, and supports the cosmological constant model.
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The abstract, sentence by sentence
Using several cosmological observations, i.e. the cosmic microwave background anisotropies (WMAP), the weak gravitational lensing (CFHTLS), the measurements of baryon acoustic oscillations (SDSS+WiggleZ), the most recent observational Hubble parameter data, the Union2.1 compilation of type Ia supernovae, and the HST prior, we impose constraints on the sum of neutrino masses ($\mnu$), the effective number of neutrino species ($\neff$) and dark energy equation of state ($w$), individually and collectively. We find that a tight upper limit on $\mnu$ can be extracted from the full data combination, if $\neff$ and $w$ are fixed. However this upper bound is severely weakened if $\neff$ and $w$ are allowed to vary. This result naturally raises questions on the robustness of previous strict upper bounds on $\mnu$, ever reported in the literature. The best-fit values from our most generalized constraint read $\mnu=0.556^{+0.231}_{-0.288}\rm eV$, $\neff=3.839\pm0.452$, and $w=-1.058\pm0.088$ at 68% confidence level, which shows a firm lower limit on total neutrino mass, favors an extra light degree of freedom, and supports the cosmological constant model. The current weak lensing data are already helpful in constraining cosmological model parameters for fixed $w$. The dataset of Hubble parameter gains numerous advantages over supernovae when $w=-1$, particularly its illuminating power in constraining $\neff$. As long as $w$ is included as a free parameter, it is still the standardizable candles of type Ia supernovae that play the most dominant role in the parameter constraints.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Using several cosmological observations, i.e. the cosmic microwave background anisotropies (WMAP), the weak gravitational lensing (CFHTLS), the measurements of baryon acoustic oscillations (SDSS+WiggleZ), the most recent observational Hubble parameter data, the Union2.1 compilation of type Ia supernovae, and the HST prior, we impose constraints on the sum of neutrino masses ($\mnu$), the effective number of neutrino species ($\neff$) and dark energy equation of state ($w$), individually and collectively. | method 0.92 | 0.91 | 0.04 | asserted 0.96 |
| s1 | We find that a tight upper limit on $\mnu$ can be extracted from the full data combination, if $\neff$ and $w$ are fixed. | result 1.00 | 0.96 | 0.18 | asserted 1.00 |
| s2 | However this upper bound is severely weakened if $\neff$ and $w$ are allowed to vary. | result 0.98 | 0.89 | 0.30 | asserted 1.00 |
| s3 | This result naturally raises questions on the robustness of previous strict upper bounds on $\mnu$, ever reported in the literature. | interpretation 0.99 | 0.17 | 0.13 | hedged possibility 0.51 |
| s4 | The best-fit values from our most generalized constraint read $\mnu=0.556^{+0.231}_{-0.288}\rm eV$, $\neff=3.839\pm0.452$, and $w=-1.058\pm0.088$ at 68% confidence level, which shows a firm lower limit on total neutrino mass, favors an extra light degree of freedom, and supports the cosmological constant model. | result 0.98 | 0.97 | 0.57 | asserted 1.00 |
| s5 | The current weak lensing data are already helpful in constraining cosmological model parameters for fixed $w$. | result 0.88 | 0.70 | 0.04 | asserted 0.85 |
| s6 | The dataset of Hubble parameter gains numerous advantages over supernovae when $w=-1$, particularly its illuminating power in constraining $\neff$. | result 0.79 | 0.78 | 0.05 | asserted 0.99 |
| s7 | As long as $w$ is included as a free parameter, it is still the standardizable candles of type Ia supernovae that play the most dominant role in the parameter constraints. | result 0.68 | 0.80 | 0.10 | asserted 0.99 |
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The paper
Original abstract
Using several cosmological observations, i.e. the cosmic microwave background anisotropies (WMAP), the weak gravitational lensing (CFHTLS), the measurements of baryon acoustic oscillations (SDSS+WiggleZ), the most recent observational Hubble parameter data, the Union2.1 compilation of type Ia supernovae, and the HST prior, we impose constraints on the sum of neutrino masses ($\mnu$), the effective number of neutrino species ($\neff$) and dark energy equation of state ($w$), individually and collectively. We find that a tight upper limit on $\mnu$ can be extracted from the full data combination, if $\neff$ and $w$ are fixed. However this upper bound is severely weakened if $\neff$ and $w$ are allowed to vary. This result naturally raises questions on the robustness of previous strict upper bounds on $\mnu$, ever reported in the literature. The best-fit values from our most generalized constraint read $\mnu=0.556^{+0.231}_{-0.288}\rm eV$, $\neff=3.839\pm0.452$, and $w=-1.058\pm0.088$ at 68% confidence level, which shows a firm lower limit on total neutrino mass, favors an extra light degree of freedom, and supports the cosmological constant model. The current weak lensing data are already helpful in constraining cosmological model parameters for fixed $w$. The dataset of Hubble parameter gains numerous advantages over supernovae when $w=-1$, particularly its illuminating power in constraining $\neff$. As long as $w$ is included as a free parameter, it is still the standardizable candles of type Ia supernovae that play the most dominant role in the parameter constraints.
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References
How the literature uses it
12 arXiv papers cite this in 13 sentences
Papers citing it · 8 sentences without a confident label
Cites it as background 5 papers
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In addition, many upper limits on the sum of the neutrino masses assume the standard model value of $$, and so do not directly apply to sterile neutrinos; however, a number of groups have constrained the $- ∑m_ν$ plane using various combinations of measurements of the CMB, Hubble constant, baryon acoustic oscillations, and galaxy clusters [ref] .
Additional Light Sterile Neutrinos and Cosmology · Partial Thermalization and Partially Relativistic Neutrinos in a $3+2$ Scenario: CMB Constraints · 0.83
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Cosmological observations play a crucial role in constraining the mass of active neutrinos (see, e.g., Refs. [ref] ).
Prospects for searching for sterile neutrinos with gravitational wave and $\gamma$-ray burst joint observations · Introduction · 0.81
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For other relevant studies of massive (active/sterile) neutrinos by using cosmological data, see, e.g., Refs. [ref] .
Constraints on active and sterile neutrinos in an interacting dark energy cosmology · Introduction · 1.00
What it cites · 46 sentences without a confident label
Contests 1 paper
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However, three problematic issues are found to affect the neutrino damping effect reproduced by this method [ref] :
Massive Neutrinos and the Non-linear Matter Power Spectrum · Observables and Data · contest 0.84
Uses the method or tool of 5 papers
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Ref. [ref] conducted a more extensive suite of N-body simulations particularly designed for quantifying precisely the suppression from massive neutrinos, and improved the original method into HALOFIT–$ν$ algorithm, [equation] with both quasi- and non-linear terms modified, and $Q_ν$ accounts for additional non-linear growth of the neutrino component [ref] .
Massive Neutrinos and the Non-linear Matter Power Spectrum · Observables and Data · 0.84
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Fortunately, people have developed numerous ways to explore those small scale phenomena, e.g. the one-loop perturbation theorem [ref] , which usually takes up the third order expansion of $P(k)$ as a close approximation, the time renormalization group flow method [ref] , and the most widely quoted HALOFIT analytical formulae as the mapping algorithm calibrated by N-body simulations [ref] , [equation] where the total power spectrum $Δ^2(k)$ is split into a quasi-linear term $Δ^2_Q$ and a pure non-linear term $Δ^2_H$.
Non-linear Power Spectrum including Massive Neutrinos: the Time-RG Flow Approach · Observables and Data · 0.83
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Fortunately, people have developed numerous ways to explore those small scale phenomena, e.g. the one-loop perturbation theorem [ref] , which usually takes up the third order expansion of $P(k)$ as a close approximation, the time renormalization group flow method [ref] , and the most widely quoted HALOFIT analytical formulae as the mapping algorithm calibrated by N-body simulations [ref] , [equation] where the total power spectrum $Δ^2(k)$ is split into a quasi-linear term $Δ^2_Q$ and a pure non-linear term $Δ^2_H$.
Nonlinear power spectrum in the presence of massive neutrinos: perturbation theory approach, galaxy bias and parameter forecasts · Observables and Data · 0.83
Uses data or values from 7 papers
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We use the most up-to-date datasets summarized by [ref] , which comprises nineteen OHD measurements over the redshift interval from $0.09≤z≤1.75$.
New constraints on cosmological parameters and neutrino properties using the expansion rate of the Universe to z~1.75 · Observational Hubble Parameter Data · 1.00
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The latest observations of WMAP seven-year pin down the 95% upper limit of $$ to $1.3 eV$ [ref] , while Planck and other next-term probes are presumably capable of pushing forward the sensitivity to $∼0.2-0.03 eV$, [ref] .
Measuring the neutrino mass from future wide galaxy cluster catalogues · Introduction · 0.95
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The latest observations of WMAP seven-year pin down the 95% upper limit of $$ to $1.3 eV$ [ref] , while Planck and other next-term probes are presumably capable of pushing forward the sensitivity to $∼0.2-0.03 eV$, [ref] .
Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation · Introduction · 0.95
Compares with 4 papers
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Including OHD, we obtain $=3.722±0.418$, which is fully consistent with Ref. [ref] ($=3.7±0.4$).
New constraints on cosmological parameters and neutrino properties using the expansion rate of the Universe to z~1.75 · Vanilla+$$ · 1.00
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(Hereafter we neglect the unit of “eV” for brevity.) This is a 10% improvement over the formerly reported upper limit given by Ref. [ref] and Ref. [ref] using similar data.
CFHTLS weak-lensing constraints on the neutrino masses · Vanilla+$$ · 1.00
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(Hereafter we neglect the unit of “eV” for brevity.) This is a 10% improvement over the formerly reported upper limit given by Ref. [ref] and Ref. [ref] using similar data.
Constraints on Neutrino Masses from Weak Lensing · Vanilla+$$ · 1.00
Cites as support 4 papers
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Moreover, we do not consider a running spectral index or any tensor contribution, for the constraint on neutrino masses is not relaxed even when they are allowed [ref] .
Robust Neutrino Constraints by Combining Low Redshift Observations with the CMB · Constraints on Cosmological Parameters · 1.00
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As also pointed out recently by Ref. [ref] , neither future CMB experiment or weak lensing shear measurement or galaxy tomographic survey alone can reach $∼5σ$ detection of a non-zero sum of neutrino masses; it is their joint analysis that effectively breaks parameter degeneracies.
Measuring neutrino masses with a future galaxy survey · Conclusion and Discussion · 0.97
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This may be persuasive in designing next generation spectroscopic surveys in pursuit of large sample OHD measurements [ref] .
Power of Observational Hubble Parameter Data: a Figure of Merit Exploration · Vanilla+$$ · 0.98
Cites as background 7 papers
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Nevertheless, the most compelling bounds on the total mass of neutrinos ($$) come from the cosmos (for recent reviews, see Refs. [ref] ).
Neutrino physics from precision cosmology · Introduction · 0.90
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Nevertheless, the most compelling bounds on the total mass of neutrinos ($$) come from the cosmos (for recent reviews, see Refs. [ref] ).
Cosmological and Astrophysical Neutrino Mass Measurements · Introduction · 0.90
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Generally speaking, three independent fitters are proposed and maintained amongst the cosmology community, i.e. SALT2 [ref] , MLCS2k2 [ref] , and SiFTO [ref] .
SiFTO: An Empirical Method for Fitting SNe Ia Light Curves · Type Ia Supernovae · 0.86
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