#### 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. • •
$2.99$ $\pm0.17$ 68 1
 2020
COSM
$2.84$ $\pm0.15$ 68 2
 2020
COSM BBN
$2.88$ $\pm0.17$ 68 3
 2020
COSM Planck and BOSS
$\text{2.3 - 3.2}$ 95 4
 2017
COSM
$2.88$ $\pm0.16$ 68 5
 2016
COSM BBN
$2.88$ $\pm0.20$ 95 6
 2015
COSM
$3.3$ $\pm0.5$ 95 7
 2014
COSM Planck
$3.78$ ${}^{+0.31}_{-0.30}$ 8
 2014
COSM
$3.29$ $\pm0.31$ 9
 2014
COSM
$<3.80$ 95 10
 2014
COSM
$<4.10$ 95 11
 2012
COSM
$<5.79$ 95 12
 2012
COSM
$<4.08$ 95
 2011
COSM BBN
$\text{0.9 - 8.2}$ 13
 2007
COSM
$\text{3 - 7}$ 95 14
 2006
COSM
$\text{2.7 - 4.6}$ 95 15
 2006
COSM
$\text{3.6 - 7.4}$ 95 14
 2006
COSM
$<4.4$ 16
 2005
COSM
$<3.3$ 17
 2003 C
COSM
$\text{1.4 - 6.8}$ 18
 2003
COSM
$\text{1.9 - 6.6}$ 18
 2003
COSM
$\text{2 - 4}$
 1999
COSM BBN
$<4.3$
 1999
COSM BBN
$<4.9$
 1997
Cosmology
$<3.6$
 1997 B
High D/H quasar abs.
$<4.0$
 1997
BBN; high ${}^{4}\mathrm {He}$ and ${}^{7}\mathrm {Li}$
$<4.7$
 1996 B
COSM High D/H quasar abs.
$<3.9$
 1996
COSM BBN; high ${}^{4}\mathrm {He}$ and ${}^{7}\mathrm {Li}$
$<4.5$
 1996
COSM High D/H quasar abs.
$<3.6$
 1995
BBN; ${}\geq{}3$ massless ${{\mathit \nu}}$
$<3.3$
 1991
Cosmology
$<3.4$
 1990
Cosmology
$<4$
 1984
Cosmology
$<4$
 1979
Cosmology
$<7$
 1977
Cosmology
 1971
Cosmology
$<16$ 19
 1969
Cosmology
 1964
Cosmology
 1 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.
 2 FIELDS 2020 combines Planck 2018 CMB data with BBN and observations of deuterium and Helium-4.
 3 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.
 4 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.
 5 CYBURT 2016 combines Planck 2015 CMB data with BBN and observations of deuterium and Helium-4.
 6 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.
 7 Fit to the number of neutrino degrees of freedom from Planck CMB data along with WMAP polarization, high L, and BAO data.
 8 Fit to the number of neutrinos degrees of freedom from Planck CMB data along with BAO, shear and cluster data.
 9 Fit based on the SPT-SZ survey combined with CMB, BAO, and ${{\mathit H}_{{0}}}$ data.
 10 Constrains the number of neutrino degrees of freedom (marginalizing over the total mass) from CMB, CMB lensing, BAO, and galaxy clustering data.
 11 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 $3.45$ $\pm0.65$.
 12 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.
 13 Constrains the number of neutrino types from recent CMB and large scale structure data. No priors on other cosmological parameters are used.
 14 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.
 15 Constrains the number of neutrino types from recent CMB and large scale structure data. See also HAMANN 2007 .
 16 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 .
 17 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{}$3 is assumed to compute the limit.
 18 95$\%$ confidence level range on the number of neutrino flavors from WMAP data combined with other CMB measurements, the 2dfGRS data, and HST data.
 19 SHVARTSMAN 1969 limit inferred from his equations.
References:
 AGHANIM 2020
AA 641 A6 Planck 2018 results. VI. Cosmological parameters
 FIELDS 2020
JCAP 2003 010 Big-Bang Nucleosynthesis after Planck
 Also
JCAP 2011 E02 (errat.) Big-Bang Nucleosynthesis after Planck
 IVANOV 2020
PR D101 083504 Cosmological Parameters and Neutrino Masses from the Final Planck and Full-Shape BOSS Data
 VERDE 2017
JCAP 1704 023 Early Cosmology Constrained
 CYBURT 2016
RMP 88 015004 Big Bang Nucleosynthesis: 2015
 ROSSI 2015
PR D92 063505 Constraints on Dark Radiation from Cosmological Probes
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AA 571 A16 Planck 2013 Results. XVI. Cosmological Parameters
 COSTANZI 2014
JCAP 1410 081 Neutrino Constraints: what Large-Scale Structure and CMB Data are Telling Us?
 HOU 2014
APJ 782 74 Constraints on Cosmology from the Cosmic Microwave Background Power Spectrum of the 2500 deg${}^{2}$ SPT-SZ Survey
 LEISTEDT 2014
PRL 113 041301 No New Cosmological Concordance with Massive Sterile Neutrinos
 MORESCO 2012
JCAP 1207 053 New Constraints on Cosmological Parameters and Neutrino Properties using the Expansion Rate of the Universe to z ~ 1.75
 XIA 2012
JCAP 1206 010 Constraints on Massive Neutrinos from the CFHTLS Angular Power Spectrum
 MANGANO 2011
PL B701 296 A Robust Upper Limit on ${{\mathit N}_{{eff}}}$ from BBN, circa 2011
 ICHIKAWA 2007
JCAP 0705 007 Constraint on the Effective Number of Neutrino Species from the WMAP and SDSS LRG Power Spectra
 CIRELLI 2006
JCAP 0612 013 Cosmology of Neutrinos and Extra-Light Particles after WMAP3
 HANNESTAD 2006
JCAP 0611 016 Neutrino Masses and Cosmic Radiation Density: Combined Analysis
 SELJAK 2006
JCAP 0610 014 Cosmological Parameters from Combining the Lyman-$\alpha$ Forest with CMB, Galaxy Clustering and SN Constraints
 CYBURT 2005
ASP 23 313 New BBN Limits on Physics Beyond the Standard Model from ${}^{4}\mathrm {He}$
 BARGER 2003C
PL B566 8 Effective Number of Neutrinos and Baryon Asymmetry from BBN and WMAP
 CROTTY 2003
PR D67 123005 Measuring the Cosmological Background of Relativistic Particles with the Wilkinson Microwave Anisotropy Probe
 PIERPAOLI 2003
MNRAS 342 L63 Constraints on the Cosmic Neutrino Background
 LISI 1999
PR D59 123520 The Big Bang Nucleosynthesis Limit on N$_{{{\mathit \nu}} }$
 OLIVE 1999
ASP 11 403 Generalized Limits to the Number of Light Particle Degrees of Freedom from Big Bang Nucleosynthesis
 COPI 1997
PR D55 3389 The Big Bang Nucleosynthesis Limit to the Number of Neutrino Species
 HATA 1997B
PR D55 540 Cosmological Implications of Two Conflicting Deuterium Abundances
 OLIVE 1997
ASP 7 27 A Big Bang Nucleosynthesis Likelihood Analysis of the Baryon to Photon Ratio and the Number of Light Particle Degrees of Freedom
 CARDALL 1996B
APJ 472 435 Big Bang Nucleosynthesis in Light of Discordant Deuterium Measurements
 FIELDS 1996
New Ast 1 77 Model Independent Predictions of Big Bang Nucleosinthesis from ${}^{4}\mathrm {He}$ and ${}^{7}\mathrm {Li}$: Consistency and Implications
 KERNAN 1996
PR D54 3681 No Crisis for Big Bang Nucleosynthesis
 OLIVE 1995
PL B354 357 A New Look at Neutrino Limits from Big Bang Nucleosynthesis
 WALKER 1991
APJ 376 51 Primordial Nucleosynthesis Redux
 OLIVE 1990
PL B236 454 Big Bang Nucleosynthesis Revisited
 YANG 1984
APJ 281 493 Primordial Nucleosynthesis: a Critical Comparison of Theory and Observation
 YANG 1979
APJ 227 697 Constraints on Cosmology and Neutrino Physics from Big Bang Nucleosynthesis
 Also
PRL 43 239 Cosmological Constraints on Superweak Particles
 STEIGMAN 1977
PL 66B 202 Cosmological Limits to the Number of Massive Leptons
 PEEBLES 1971
Physical Cosmology Physical Cosmology (Princeton, 1971) Book. (294p.)
 SHVARTSMAN 1969
JETPL 9 184 Density of Relict Particles with Zero Rest Mass in the Universe
 HOYLE 1964
NAT 203 1108 The Mystery of the Cosmic Helium Abundance