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Limits from Astrophysics and Cosmology

Effective Number of Light ${{\mathit \nu}}$ Types

“Light” means here with a mass $<$ about 1 MeV. The quoted values correspond to N$_{{\mathrm {eff}}}$, where N$_{{\mathrm {eff}}}$ = 3.045 in the Standard Model with N$_{{{\mathit \nu}}}$ = 3. See also reviews on "Big-Bang Nucleosynthesis" and "Neutrinos in Cosmology."

VALUE

CL%

DOCUMENT ID

TECN

COMMENT

• • We do not use the following data for averages, fits, limits, etc. • •

$3.12$ $\pm0.38$

95

COSM

BOSS, eBOSS, CMB

$2.90$ $\pm0.15$

68

COSM

BOSS + CMB

$2.89$ $\pm0.14$

68

COSM

BBN + CMB

$2.99$ $\pm0.17$

68

COSM

$2.84$ $\pm0.15$

68

COSM

BBN

$2.88$ $\pm0.17$

68

COSM

Planck and BOSS

$\text{2.3 - 3.2}$

95

COSM

$2.88$ $\pm0.16$

68

COSM

BBN

$2.88$ $\pm0.20$

95

COSM

$3.3$ $\pm0.5$

95

COSM

Planck

$3.78$ ${}^{+0.31}_{-0.30}$

COSM

$3.29$ $\pm0.31$

COSM

$<3.80$

95

COSM

$<4.10$

95

COSM

$<5.79$

95

COSM

$<4.08$

95

COSM

BBN

$\text{0.9 - 8.2}$

COSM

$\text{3 - 7}$

95

COSM

$\text{2.7 - 4.6}$

95

COSM

$\text{3.6 - 7.4}$

95

COSM

$<4.4$

COSM

$<3.3$

COSM

$\text{1.4 - 6.8}$

COSM

$\text{1.9 - 6.6}$

COSM

$\text{2 - 4}$

COSM

BBN

$<4.3$

COSM

BBN

$<4.9$

Cosmology

$<3.6$

High D/H quasar abs.

$<4.0$

BBN; high ${}^{4}\mathrm {He}$ and ${}^{7}\mathrm {Li}$

$<4.7$

COSM

High D/H quasar abs.

$<3.9$

COSM

BBN; high ${}^{4}\mathrm {He}$ and ${}^{7}\mathrm {Li}$

$<4.5$

COSM

High D/H quasar abs.

$<3.6$

BBN; ${}\geq{}3$ massless ${{\mathit \nu}}$

$<3.3$

Cosmology

$<3.4$

Cosmology

$<4$

Cosmology

$<4$

Cosmology

$<7$

Cosmology

Cosmology

$<16$

Cosmology

Cosmology

¹	BRIEDEN 2022 combines large scale structure data from BOSS and eBOSS including the shape of the matter power spectrum with Planck CMB data.

²	KUMAR 2022 combine the reconstructed galaxy power spectrum from BOSS data with Planck CMB data.

³	YEH 2022 combines Planck 2018 CMB data with BBN and observations of deuterium and ${}^{}\mathrm {Helium}$-4. Supersedes FIELDS 2020.

⁴	AGHANIM 2020 best fit on number of neutrino types is based on Planck data combined with lensing and baryon acoustic oscillations (BAO). Without BAO, they find $2.89$ ${}^{+0.18}_{-0.19}$. Several other values are quoted using different combinations of data.

⁵	FIELDS 2020 combines Planck 2018 CMB data with BBN and observations of deuterium and Helium-4.

⁶	IVANOV 2020 combines 2018 Planck CMB data with baryon acoustic oscillation data from BOSS. This study is based on a full-shape likelhood for the redshift-space galaxy power spectrum of the BOSS data.

⁷	Uses Planck Data combined with an independent standard measure of distance to the sound horizon to set a limit on the total number of neutrinos. Only CMB and early-time information are used.

⁸	CYBURT 2016 combines Planck 2015 CMB data with BBN and observations of deuterium and Helium-4.

⁹	ROSSI 2015 sets limits on the number of neutrino types using BOSS Lyman alpha forest data combined with Planck CMB data and baryon acoustic oscillations.

¹⁰	Fit to the number of neutrino degrees of freedom from Planck CMB data along with WMAP polarization, high L, and BAO data.

¹¹	Fit to the number of neutrinos degrees of freedom from Planck CMB data along with BAO, shear and cluster data.

¹²	Fit based on the SPT-SZ survey combined with CMB, BAO, and ${{\mathit H}_{{{0}}}}$ data.

¹³	Constrains the number of neutrino degrees of freedom (marginalizing over the total mass) from CMB, CMB lensing, BAO, and galaxy clustering data.

¹⁴	Limit on the number of light neutrino types from observational Hubble parameter data with seven-year WMAP data, SPT, and the most recent estimate of ${{\mathit H}_{{{0}}}}$. Best fit is $3.45$ $\pm0.65$.

¹⁵	Limit on the number of light neutrino types from the CFHTLS combined with seven-year WMAP data and a prior on the Hubble parameter. Best fit is $4.17$ ${}^{+1.62}_{-1.26}$. Limit is relaxed to $3.98$ ${}^{+2.02}_{-1.20}$ when small scales affected by non-linearities are removed.

¹⁶	Constrains the number of neutrino types from recent CMB and large scale structure data. No priors on other cosmological parameters are used.

¹⁷	Constrains the number of neutrino types from recent CMB, large scale structure, Lyman-alpha forest, and SN1a data. The slight preference for $\mathit N_{{{\mathit \nu}}}$ $>$ 3 comes mostly from the Lyman-alpha forest data.

¹⁸	Constrains the number of neutrino types from recent CMB and large scale structure data. See also HAMANN 2007.

¹⁹	Limit on the number of neutrino types based on ${}^{4}\mathrm {He}$ and D/H abundance assuming a baryon density fixed to the WMAP data. Limit relaxes to 4.6 if D/H is not used or to 5.8 if only D/H and the CMB are used. See also CYBURT 2001 and CYBURT 2003.

²⁰	Limit on the number of neutrino types based on combination of WMAP data and big-bang nucleosynthesis. The limit from WMAP data alone is 8.3. See also KNELLER 2001. $\mathit N_{{{\mathit \nu}}}{}\geq{}$3 is assumed to compute the limit.

²¹	95$\%$ confidence level range on the number of neutrino flavors from WMAP data combined with other CMB measurements, the 2dfGRS data, and HST data.

²²	SHVARTSMAN 1969 limit inferred from his equations.

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