$\bf{<6 \times 10^{32}}$ 
^{ 1} 

YUKA 
• • • We do not use the following data for averages, fits, limits, etc. • • • 
$<6.8 \times 10^{23}$ 


YUKA 
$<1.4 \times 10^{29}$ 
^{ 2} 

YUKA 
$<5 \times 10^{30}$ 
^{ 3} 

YUKA 
$<3 \times 10^{30}$ 
^{ 3} 

YUKA 
$<1.3 \times 10^{29}$ 
^{ 3} 

YUKA 
$<6 \times 10^{30}$ 
^{ 4} 

YUKA 
$<8 \times 10^{30}$ 
^{ 5} 

YUKA 
$<7 \times 10^{23}$ 
^{ 6} 

DISP 
$<1.2 \times 10^{22}$ 
^{ 6} 

DISP 
$<2.9 \times 10^{21}$ 
^{ 7} 

YUKA 
$<5 \times 10^{23}$ 
^{ 8} 


$<4 \times 10^{25}$ 
^{ 9} 


$<6 \times 10^{32}$ 
^{ 10} 

YUKA 
$<9.0 \times 10^{34}$ 
^{ 11} 


$>6 \times 10^{34}$ 
^{ 12} 


$<8 \times 10^{20}$ 
^{ 13}^{, 14} 

DISP 

^{ 15}^{, 14} 


$<7 \times 10^{23}$ 


YUKA 
$<2 \times 10^{29} \mathit h{}^{1}_{0}$ 



$<7 \times 10^{28}$ 



$<8 \times 10^{4}$ 



^{1}
CHOUDHURY 2004 concludes from a study of weaklensing data that masses heavier than about the inverse of 100 Mpc seem to be ruled out if the gravitation field has the Yukawa form.

^{2}
DESAI 2018 limit based on dynamical mass models of galaxy cluster Abell 1689.

^{3}
GUPTA 2018 obtains graviton mass limits using stacked clusters from 3 disparate surveys.

^{4}
RANA 2018 limit, 68$\%$ CL, obtained using weak lensing mass profiles out to the radius at which the cluster density falls to 200 times the critical density of the Universe. Limit is based on the fractional change between Newtonian and Yukawa accelerations for the 50 most massive galaxy clusters in the Local Cluster Substructure Survey. Limits for other CL's and other density cuts are also given.

^{5}
RANA 2018 limit, 68$\%$ CL, obtained using mass measurements via the SZ effect out to the radius 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.

^{6}
ABBOTT 2016 and ABBOTT 2017 assumed a dispersion relation for gravitational waves modified relative to GR.

^{7}
ZAKHAROV 2016 constrains range of Yukawa gravity interaction from S2 star orbit about black hole at Galactic center. The limit is $<$ $2.9 \times 10^{21}$ eV for $\delta $ = 100.

^{8}
BRITO 2013 explore massive graviton (spin2) fluctuations around rotating black holes.

^{9}
BASKARAN 2008 consider fluctuations in pulsar timing due to photon interactions (``surfing'') with background gravitational waves.

^{10}
GRUZINOV 2005 uses the DGP model (DVALI 2000 ) showing that nonperturbative effects restore continuity with Einstein's equations as the gravition mass approaches 0, then bases his limit on Solar System observations.

^{11}
GERSHTEIN 2004 use nonEinstein field relativistic theory of gravity (RTG), with a massive graviton, to obtain the 95$\%$ CL mass limit implied by the value of $\Omega _{tot}$ = $1.02$ $\pm0.02$ current at the time of publication.

^{12}
DVALI 2003 suggest scale of horizon distance via DGP model (DVALI 2000 ). For a horizon distance of $3 \times 10^{26}$ m (about age of Universe/$\mathit c$; GOLDHABER 2010 ) this graviton mass limit is implied.

^{13}
FINN 2002 analyze the orbital decay rates of PSR$~$B1913+16 and PSR$~$B1534+12 with a possible graviton mass as a parameter. The combined frequentist mass limit is at 90$\%$CL.

^{14}
As of 2014, limits on dP/dt are now about 0.1$\%$ (see T. Damour, ``Experimental tests of gravitational theory,'' in this $\mathit Review$).

^{15}
DAMOUR 1991 is an analysis of the orbital period change in binary pulsar PSR$~1913+$16, and confirms the general relativity prediction to $0.8\%$. ``The theoretical importance of the [rate of orbital period decay] measurement has long been recognized as a direct confirmation that the gravitational interaction propagates with velocity $\mathit c$ (which is the immediate cause of the appearance of a damping force in the binary pulsar system) and thereby as a test of the existence of gravitational radiation and of its quadrupolar nature.'' TAYLOR 1993 adds that orbital parameter studies now agree with general relativity to $0.5\%$, and set limits on the level of scalar contribution in the context of a family of tensor [spin$~$2]biscalar theories.
