Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

graviton

J = 2graviton MASS
It is likely that the graviton is massless. More than fifty years ago Van
Dam and Veltman (VANDAM 70), Iwasaki (IWASAKI 70), and Zakharov(ZAKHAROV 70) almost simultaneously showed that in the linear approximation a theory with a finite graviton mass does not approach GR as themass approaches zero. Attempts have been made to evade this ”vDVZ discontinuity” by invoking modified gravity or nonlinear theory by De Rahm(DE-RHAM 17) and others. More recently, the analysis of gravitational
wave dispersion has led to bounds that are largely independent of the underlying model, even if not the strongest. We quote the best of these as
our best limit.
Experimental limits have been set based on a Yukawa potential (YUKA),
dispersion relation (DISP), or other modified gravity theories (MGRV).
The following conversions are useful: 1 eV = 1.783 × 10−33 g = 1.957 ×
10−6 m e ; λ̄
¯C = (1.973 × 10−7 m)×(1 eV/m g ).
VALUE (eV)DOCUMENT ID

TECNCOMMENT

1 ABBOTT<1.76 × 10−23
21 DISP LIGO Virgo catalog GWTC-2• • • We do not use the following data for averages, fits, limits, etc. • • •2 DEFELICE<8× 10−34
21 MGRV Normal branch Minimal Theory ofMassive Gravity
3 BERNUS<3.2 × 10−23
20 YUKA Planetary ephemeris INPOP19a4 SHAO
<2× 10−28
20 DISP Binary pulsar Galileon radiation−235<4.7 × 10
ABBOTT
19 DISP LIGO Virgo catalog GWTC-1
6 BERNUS<7× 10−23
19 YUKA Planetary ephemeris INPOP17b7 MIAO
<3.1 × 10−20
19 DISP Binary pulsar orbital decay rate
8 DESAI<1.4 × 10−29
18 YUKA Gal cluster Abell 1689−309<5× 10GUPTA
18 YUKA Using SPT-SZ
9 GUPTA
<3× 10−30
18 YUKA Using Planck all-sky SZ
9 GUPTA<1.3 × 10−29
18 YUKA Using redMaPPer SDSS-DR8−3010<6× 10RANA
18 YUKA Weak lensing in massive clusters
11 RANA<8× 10−30
18 YUKA SZ effect in massive clusters−2312<1.0 × 10WILL
18 YUKA Perihelion advances of planets
5 ABBOTT<7× 10−23
17 DISP Combined dispersion limit fromthree BH mergers
5 ABBOTT<1.2 × 10−22
16 DISP Combined dispersion limit fromtwo BH mergers
13 ZAKHAROV 16 YUKA S2 star orbit<2.9 × 10−21
14 BRITO<5× 10−23
13 MGRV Spinning black holes bounds−3215<6× 10GRUZINOV
05 MGRV Solar System observations
16 CHOUDHURY 04 YUKA Weak gravitational lensing<6× 10−32−34
17<9.0 × 10
GERSHTEIN 04 MGRV From Ωtot value assuming RTG−2018,19<8× 10FINN
02 DISP Binary pulsar orbital period decrease<7× 10−23TALMADGE 88 YUKA Solar system planetary astrometricdata

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

20 GOLDHABER 74 YUKA Rich clusters<1.3 × 10−29−28<7× 10HARE73 YUKA Galaxy<8× 104
HARE73 YUKA 2γ decay
1 ABBOTT 21 assumed modified gravitational-wave dispersion to establish a limit on
graviton mass, using LIGO-Virgo O1-O3a binary black hole (BBH) events.
2 DEFELICE 21 studies the normal branch of the Minimal Theory of Massive Gravity(MTMG) to find that after five parameters are adjusted to obtain agreement with all+ 4.5 ) × 10−67 eV2 or m <presently available data, today’s squared mass m2 = (2.5 −g
4.8g−33
8.4 × 10eV, both at the 95% CL.
3 BERNUS 20 use the latest solution of the ephemeris INPOP (19a) in order to improvethe constraint in BERNUS 19 on the existence of a Yukawa suppression to the Newtonian
potential, generically associated to a gravitons mass.
4 SHAO 20 sets limit, 95% CL, based on non-observation of excess gravitational radiationin 14 well-timed binary pulsars in the context of the cubic Galileon model.
5 ABBOTT 19, ABBOTT 17, and ABBOTT 16 assumed modified gravitational waves
dispersion to establish limits on graviton mass.
6 BERNUS 19 use the planetary ephemeris INPOP 17b to constraint the existence of a
Yukawa suppression to the Newtonian potential, generically associated to a gravitonsmass.
7 MIAO 19 90% CL limit is based on orbital period decay rates of 9 binary pulsars using a
Bayesian prior uniform in graviton mass. Limit becomes < 5.2 × 10−21 eV for a prioruniform in ln(m g ).
8 DESAI 18 limit based on dynamical mass models of galaxy cluster Abell 1689.
9 GUPTA 18 obtains graviton mass limits using stacked clusters from 3 disparate surveys.
10 RANA 18 limit, 68% CL, obtained using weak lensing mass profiles out to the radius atwhich the cluster density falls to 200 times the critical density of the Universe. Limit isbased on the fractional change between Newtonian and Yukawa accelerations for the 50
most massive galaxy clusters in the Local Cluster Substructure Survey. Limits for otherCL’s and other density cuts are also given.
11 RANA 18 limit, 68% CL, obtained using mass measurements via the SZ effect out to theradius at which the cluster density falls to 500 times the critical density of the Universe
for 182 optically confirmed galaxy clusters in an Altacama Cosmology Telescope survey.
Limits for other CL’s and other density cuts are also given.
12 WILL 18 limit from perihelion advances of the planets, notably Earth, Mars, and Saturn.
Alternate analysis yields < 6 × 10−24 .
13 ZAKHAROV 16 constrains range of Yukawa gravity interaction from S2 star orbit about
black hole at Galactic center. The limit is < 2.9 × 10−21 eV for δ = 100.
14 BRITO 13 explore massive graviton (spin-2) fluctuations around rotating black holes.
15 GRUZINOV 05 uses the DGP model (DVALI 00) showing that non-perturbative effects
restore continuity with Einstein’s equations as the gravition mass approaches zero, thenbases his limit on Solar System observations.
16 CHOUDHURY 04 concludes from a study of weak-lensing data that masses heavier thanabout the inverse of 100 Mpc seem to be ruled out if the gravitation field has the Yukawaform.
17 GERSHTEIN 04 use non-Einstein field relativistic theory of gravity (RTG), with a massivegraviton, to obtain the 95% CL mass limit implied by the value of Ωtot = 1.02 ± 0.02
current at the time of publication.
18 FINN 02 analyze the orbital decay rates of PSR B1913+16 and PSR B1534+12 with apossible graviton mass as a parameter. The combined frequentist mass limit is at 90%CL.
19 As of 2020, limits on dP/dt are now about 0.1% (see T. Damour, “Experimental testsof gravitational theory,” in this Review).
20 GOLDHABER 74 establish this limit considering the binding of galactic clusters, corrected
to Planck h0 = 0.67.

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

graviton REFERENCESABBOTT
DEFELICEBERNUSSHAOABBOTTBERNUS
MIAO
DESAI
GUPTA
RANA
WILL
ABBOTT
DE-RHAMABBOTTZAKHAROVBRITOGRUZINOVCHOUDHURYGERSHTEIN

21212020191919181818181717161613050404

FINN
DVALI
TALMADGE
GOLDHABERHARE
IWASAKIVANDAMZAKHAROV

0200
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