This is a sum of the neutrino masses, ${\mathit m}_{\mathrm {tot}}$, as defined in the above note, of effectively stable neutrinos, i.e. those with mean lifetimes on cosmological scales. When necessary, we have generalized the results reported so they apply to ${\mathit m}_{\mathrm {tot}}$. For other limits, see SZALAY 1976, VYSOTSKY 1977, BERNSTEIN 1981, FREESE 1984, SCHRAMM 1984, and COWSIK 1985. For more information see a note on "Neutrinos in Cosmology" in this $\mathit Review$.

VALUE (eV) CL% DOCUMENT ID TECN  COMMENT • • We do not use the following data for averages, fits, limits, etc. • • $<0.082$ 95 1 BRIEDEN 2022 COSM BOSS, eBOSS, and CMB $<0.116$ 95 2 KUMAR 2022 COMS BOSS and CMB $<0.14$ 95 3 TANSERI 2022 COSM BOSS and CMB $<0.13$ 95 4 ABBOTT 2021 A COSM DES and Planck $<0.12$ 95 5 ALAM 2021 COSM $<0.09$ 95 6 DI-VALENTINO 2021 COSM $<0.16$ 95 7 GARNY 2021 COSM $\text{< 0.06 - 0.14}$ 95 8 STOCKER 2021 COSM Normal mass ordering $<0.12$ 95 9 AGHANIM 2020 COSM $<0.15$ 95 10 CHOUDHURY 2020 COSM Normal mass hierarchy $<0.16$ 95 11 IVANOV 2020 COSM Planck and BOSS $<0.11$ 95 12 PALANQUE-DELA.. 2020 COSM Lyman alpha and CMB $<0.26$ 95 13 LOUREIRO 2019 COSM $<0.18$ 95 14 UPADHYE 2019 COSM BOSS and CMB $<0.152$ 95 15 CHOUDHURY 2018 COSM $0.064$ ${}^{+0.061}_{-0.005}$ 95 16 SIMPSON 2017 COSM $<0.14$ 95 17 YECHE 2017 COSM BOSS and XQ-100 $<0.0926$ 90 18 DIVALENTINO 2016 COSM $<0.18$ 95 19 HUANG 2016 COSM Normal mass hierarchy $<0.14$ 95 20 ROSSI 2015 COSM $<0.23$ 95 21 ADE 2014 COSM Planck $0.320$ $\pm0.081$ 22 BATTYE 2014 COSM $0.35$ $\pm0.10$ 23 BEUTLER 2014 COSM BOSS $0.22$ ${}^{+0.09}_{-0.10}$ 24 COSTANZI 2014 COSM $0.32$ $\pm0.11$ 25 HOU 2014 COSM $<0.26$ 95 26 LEISTEDT 2014 COSM $<0.18$ 95 27 RIEMER-SORENS.. 2014 COSM $<0.24$ 68 28 MORESCO 2012 COSM $<0.29$ 95 29 XIA 2012 COSM $<0.81$ 95 30 SAITO 2011 COSM SDSS $<0.44$ 95 31 HANNESTAD 2010 COSM $<0.6$ 95 32 SEKIGUCHI 2010 COSM $<0.28$ 95 33 THOMAS 2010 COSM $<1.1$ 34 ICHIKI 2009 COSM $<1.3$ 95 35 KOMATSU 2009 COSM WMAP $<1.2$ 36 TERENO 2009 COSM $<0.33$ 37 VIKHLININ 2009 COSM $<0.28$ 38 BERNARDIS 2008 COSM $\text{< 0.17 - 2.3}$ 39 FOGLI 2007 COSM $<0.42$ 95 40 KRISTIANSEN 2007 COSM $\text{< 0.63 - 2.2}$ 41 ZUNCKEL 2007 COSM $<0.24$ 95 42 CIRELLI 2006 COSM $<0.62$ 95 43 HANNESTAD 2006 COSM $<1.2$ 44 SANCHEZ 2006 COSM $<0.17$ 95 42 SELJAK 2006 COSM $<2.0$ 95 45 ICHIKAWA 2005 COSM $<0.75$ 46 BARGER 2004 COSM $<1.0$ 47 CROTTY 2004 COSM $<0.7$ 48 SPERGEL 2003 COSM WMAP $<0.9$ 49 LEWIS 2002 COSM $<4.2$ 50 WANG 2002 COSM CMB $<2.7$ 51 FUKUGITA 2000 COSM $<5.5$ 52 CROFT 1999 ASTR ${}^{}\mathrm {Ly}$ $\alpha $ power spec $<180$ SZALAY 1974 COSM $<132$ COWSIK 1972 COSM $<280$ MARX 1972 COSM $<400$ GERSHTEIN 1966 COSM 1  BRIEDEN 2022 combines redshift-space distortions and the shape of the matter power spectrum from BOSS and eBOSS data together with Planck CMB data. Absent the CMB data, the limit is 0.40 eV. 2  KUMAR 2022 combine the reconstructed galaxy power spectrum from BOSS data with Planck CMB data. 3  TANSERI 2022 combines BOSS galaxy clustering data with measurements of CMB data. Updates VAGNOZZI 2017. 4  ABBOTT 2021A combines Dark Energy Survey (DES) year 3 results with Planck CMB lensing measurements. 5  ALAM 2021 limit on the sum of neutrino masses by the eBOSS collaboration is based on galaxy, quasar, and Lyman-${{\mathit \alpha}}$ 3D clustering data combined with Planck temperature and polarization CMB and supernovae data. 6  DI-VALENTINO 2021 combines CMB temperature and polarization, SNIa luminosity distances and baryon acoustic oscillations data. 7  GARNY 2021 employs a model for the Lyman-${{\mathit \alpha}}$ flux power spectrum to set a limit using BOSS data. When combined with Planck CMB temperature and polarization data, a 95$\%$ CL range $0.10 - 0.13$ eV is found. 8  STOCKER 2021 use terrestrial and cosmological experiments to set a 95$\%$ CL range on the sum of neutrino masses of $0.058 - 0.139$ eV for normal ordering and $0.098 - 0.174$ eV for inverse ordering. They also set an upper limit of 0.037 eV (NO) and 0.042 eV (IO) for the lightest neutrino mass. 9  AGHANIM 2020 limit on the sum of neutrino masses from Planck data combined with lensing and baryon acoustic oscillations (BAO). Without BAO, the limit relaxes to $<0.24~$eV. Several other limits are quoted based on different combinations of data. 10  CHOUDHURY 2020 combines 2018 Planck CMB temperature and polarization data plus lensing, together with baryon acoustic oscillation data from BOSS, MGS, and 6dFGS. Assumes $\Lambda CDM$ model. The upper limit is 0.17 eV for the inverted hierarchy, and 0.12 eV for degenerate neutrinos. Limits are also derived for extended cosmological models. 11  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. 12  PALANQUE-DELABROUILLE 2020 combine Lyman alpha and Planck temperature and polarization data. Limit improves to 0.09 eV when CMB lensing and baryon acoustic oscillation data are included. 13  LOUREIRO 2019 combines data from large scale structure, cosmic microwave background, type Ia supernovae and big bang nucleosynthesis using physically motivated neutrino mass models. 14  UPADHYE 2019 uses the shape of the BOSS redshift-space galaxy power spectrum in combination with the CMB, and supernovae data. Limit weakens to $<$ 0.54 eV if the dark energy equation of state is allowed to vary. 15  CHOUDHURY 2018 combines 2015 Planck CMB temperature data, information from the optical depth to reionization from Planck 2016 intermediate results together with baryon acoustic oscillation data from BOSS, MGS, and 6dFGS as well as supernovae Type Ia data from the Pantheon Sample. The limit is strengthened to 0.118 eV when high-$\mathit l$ CMB polarization data is also included. 16  SIMPSON 2017 uses a combination of laboratory and cosmological measurements to determine the light neutrino masses and argue that there is strong evidence for the normal mass ordering. 17  Constrains the total mass of neutrinos using the Lyman-alpha forest power spectrum with BOSS (mid-resolution), XQ-100 (high-resolution) and CMB. Without the CMB data, the limit relaxes to 0.8 eV. Supersedes PALANQUE-DELABROUILLE 2015A. 18  Constrains the total mass of neutrinos from Planck CMB data combined with baryon acoustic oscillation and Planck cluster data. 19  Constrains the total mass of neutrinos from BAO data from SDSS-III/BOSS combined with CMB data from Planck. Limit quoted for normal mass hierarchy. The limit for the inverted mass hierarchy is 0.20 eV and for the degenerate mass hierarchy it is 0.15 eV. 20  ROSSI 2015 sets limits on the sum of neutrino masses using BOSS Lyman alpha forest data combined with Planck CMB data and baryon acoustic oscillations. 21  Constrains the total mass of neutrinos from Planck CMB data along with WMAP polarization, high L, and BAO data. 22  Finite neutrino mass fit to resolve discrepancy between CMB and lensing measurements. 23  Fit to the total mass of neutrinos from BOSS data along with WMAP CMB data and data from other BAO constraints and weak lensing. 24  Fit to the total mass of neutrinos from Planck CMB data along with BAO. 25  Fit based on the SPT-SZ survey combined with CMB, BAO, and ${{\mathit H}_{{{0}}}}$ data. 26  Constraints the total mass of neutrinos (marginalizing over the effective number of neutrino species) from CMB, CMB lensing, BAO, and galaxy clustering data. 27  Constrains the total mass of neutrinos from Planck CMB data combined with baryon acoustic oscillation data from BOSS, 6dFGS, SDSS, WiggleZ data on the galaxy power spectrum, and HST data on the Hubble parameter. The limit is increased to 0.25 eV if a lower bound to the sum of neutrino masses of 0.04 eV is assumed. 28  Constrains the total mass of neutrinos from observational Hubble parameter data with seven-year WMAP data and the most recent estimate of ${{\mathit H}_{{{0}}}}$. 29  Constrains the total mass of neutrinos from the CFHTLS combined with seven-year WMAP data and a prior on the Hubble parameter. Limit is relaxed to 0.41 eV when small scales affected by non-linearities are removed. 30  Constrains the total mass of neutrinos from the Sloan Digital Sky Survey and the five-year WMAP data. 31  Constrains the total mass of neutrinos from the 7-year WMAP data including SDSS and HST data. Limit relaxes to 1.19 eV when CMB data is used alone. Supersedes HANNESTAD 2006. 32  Constrains the total mass of neutrinos from a combination of CMB data, a recent measurement of ${{\mathit H}_{{{0}}}}$ (SHOES), and baryon acoustic oscillation data from SDSS. 33  Constrains the total mass of neutrinos from SDSS MegaZ LRG DR7 galaxy clustering data combined with CMB, HST, supernovae and baryon acoustic oscillation data. Limit relaxes to 0.47 eV when the equation of state parameter, $\mathit w$ ${}\not=$ 1. 34  Constrains the total mass of neutrinos from weak lensing measurements when combined with CMB. Limit improves to 0.54 eV when supernovae and baryon acoustic oscillation observations are included. Assumes $\Lambda CDM$ model. 35  Constrains the total mass of neutrinos from five-year WMAP data. Limit improves to 0.67 eV when supernovae and baryon acoustic oscillation observations are included. Limits quoted assume the $\Lambda CDM$ model. Supersedes SPERGEL 2007. 36  Constrains the total mass of neutrinos from weak lensing measurements when combined with CMB. Limit improves to 0.03 $<\Sigma {\mathit m}_{{{\mathit \nu}}}<$ 0.54 eV when supernovae and baryon acoustic oscillation observations are included. The slight preference for massive neutrinos at the two-sigma level disappears when systematic errors are taken into account. Assumes $\Lambda CDM$ model. 37  Constrains the total mass of neutrinos from recent Chandra X-ray observations of galaxy clusters when combined with CMB, supernovae, and baryon acoustic oscillation measurements. Assumes flat universe and constant dark-energy equation of state, $\mathit w$. 38  Constraints the total mass of neutrinos from recent CMB and SOSS LRG power spectrum data along with bias mass relations from SDSS, DEEP2, and Lyman-Break Galaxies. It assumes $\Lambda CDM$ model. Limit degrades to 0.59 eV in a more general wCDM model. 39  Constrains the total mass of neutrinos from neutrino oscillation experiments and cosmological data. The most conservative limit uses only WMAP three-year data, while the most stringent limit includes CMB, large-scale structure, supernova, and Lyman-alpha data. 40  Constrains the total mass of neutrinos from recent CMB, large scale structure, SN1a, and baryon acoustic oscillation data. The limit relaxes to 1.75 when WMAP data alone is used with no prior. Paper shows results with several combinations of data sets. Supersedes KRISTIANSEN 2006. 41  Constrains the total mass of neutrinos from the CMB and the large scale structure data. The most conservative limit is obtained when generic initial conditions are allowed. 42  Constrains the total mass of neutrinos from recent CMB, large scale structure, Lyman-alpha forest, and SN1a data. 43  Constrains the total mass of neutrinos from recent CMB and large scale structure data. See also GOOBAR 2006. Superseded by HANNESTAD 2010. 44  Constrains the total mass of neutrinos from the CMB and the final 2dF Galaxy Redshift Survey. 45  Constrains the total mass of neutrinos from the CMB experiments alone, assuming $\Lambda $CDM Universe. FUKUGITA 2006 show that this result is unchanged by the 3-year WMAP data. 46  Constrains the total mass of neutrinos from the power spectrum of fluctuations derived from the Sloan Digital Sky Survey and the 2dF galaxy redshift survey, WMAP and 27 other CMB experiments and measurements by the HST Key project. 47  Constrains the total mass of neutrinos from the power spectrum of fluctuations derived from the Sloan Digital Sky Survey, the 2dF galaxy redshift survey, WMAP and ACBAR. The limit is strengthened to 0.6 eV when measurements by the HST Key project and supernovae data are included. 48  Constrains the fractional contribution of neutrinos to the total matter density in the Universe from WMAP data combined with other CMB measurements, the 2dfGRS data, and Lyman $\alpha $ data. The limit does not noticeably change if the Lyman $\alpha $ data are not used. 49  LEWIS 2002 constrains the total mass of neutrinos from the power spectrum of fluctuations derived from the CMB, HST Key project, 2dF galaxy redshift survey, supernovae type$~$Ia, and BBN. 50  WANG 2002 constrains the total mass of neutrinos from the power spectrum of fluctuations derived from the CMB and other cosmological data sets such as galaxy clustering and the Lyman $\alpha $ forest. 51  FUKUGITA 2000 is a limit on neutrino masses from structure formation. The constraint is based on the clustering scale $\sigma _{8}$ and the COBE normalization and leads to a conservative limit of $0.9~$eV assuming 3$~$nearly degenerate neutrinos. The quoted limit is on the sum of the light neutrino masses. 52  CROFT 1999 result based on the power spectrum of the ${}^{}\mathrm {Ly}$ $\alpha $ forest. If $\Omega _{{\mathrm {matter}}}<0.5$, the limit is improved to ${\mathit m}_{{{\mathit \nu}}}<2.4$ ($\Omega _{{\mathrm {matter}}}/0.17 - 1$) eV.

References