Limit on graviton mass using stacked galaxy cluster catalogs from SPT-SZ, Planck-SZ and SDSS-redMaPPer

In the last few years, there has been a resurgence of interest in obtaining observational bounds on the graviton mass, following the detection of gravitational waves, because of the versatility of massive graviton theories in resolving multiple problems in cosmology and fundamental physics. In this work, we apply the method proposed in Rana et al.(arXiv:1801.03309), which consists of looking for Yukawa-like fall off in the gravitational potential, to stacked galaxy cluster catalogs from three disparate surveys. These include catalogs from 2500 sq. degree SPT-SZ survey, the Planck all-sky SZ catalog, and a redMaPPer selected catalog from 10,000 sq. degree of SDSS-DR8 data. The 90\% c.l. limits which we obtained on the graviton mass using SPT, Planck and SDSS are: $m_g < 4.73 \times 10^{-30}$ eV, $3.0 \times 10^{-30}$ eV, and $1.27 \times 10^{-30}$ eV respectively; or in terms of Compton wavelength are $\lambda_g >2.62 \times 10^{20}$ km, $4.12 \times 10^{20}$ km, $9.76 \times 10^{20}$ km. These limits are about five times more stringent than the previous best bound from galaxy clusters.