To date , the only limit on graviton mass using galaxy clusters was obtained by Goldhaber and Nieto in 1974 , using the fact that the orbits of galaxy clusters are bound and closed , and extend up to 580 kpc .
From positing that only a Newtonian potential gives rise to such stable bound orbits , a limit on the graviton mass m _ { g } < 1.1 \times 10 ^ { -29 } eV was obtained ( ) .
Recently , it has been shown that one can obtain closed bound orbits for Yukawa potential ( ) , thus invalidating the main ansatz used in Ref . ( ) to obtain the graviton mass bound .
In order to obtain a revised estimate using galaxy clusters , we use dynamical mass models of the Abell 1689 ( A1689 ) galaxy cluster to check their compatibility with a Yukawa gravitational potential .
We use the mass models for the gas , dark matter , and galaxies for A1689 from Refs . ( ) , who used this cluster to test various alternate gravity theories , which dispense with the need for dark matter .
We quantify the deviations in the acceleration profile using these mass models assuming a Yukawa potential and that obtained assuming a Newtonian potential by calculating the \chi ^ { 2 } residuals between the two profiles .
Our estimated bound on the graviton mass ( m _ { g } ) is thereby given by , m _ { g } < 1.37 \times 10 ^ { -29 } eV or in terms of the graviton Compton wavelength of , \lambda _ { g } > 9.1 \times 10 ^ { 19 } km at 90 % confidence level .