No abstract

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. [1], 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: mg < 4.73 × 10 −30 eV, 3.0 × 10 −30 eV, and 1.27 × 10 −30 eV respectively; or in terms of Compton wavelength are λg > 2.62 × 10 20 km, 4.12 × 10 20 km, 9.76 × 10 20 km. These limits are about five times more stringent than the previous best bound from galaxy clusters.

We present new limits on the graviton Compton wavelength in a Yukawa potential using a sample of 12 relaxed galaxy clusters, for which the temperature and gas density profiles were derived by Vikhlinin et al [1] using Chandra X-ray observations. These limits can be converted to a bound on the graviton mass, assuming a non-zero graviton mass would lead to a Yukawa potential at these scales. For this purpose, we first calculate the total dynamical mass from the hydrostatic equilibrium equation in Yukawa gravity and then compare it with the corresponding mass in Newtonian gravity. We calculate a 90 % c.l. lower/upper limit on the graviton Compton wavelength/ mass for each of the 12 clusters in the sample. The best limit is obtained for Abell 2390, corresponding to λg > 3.58×10 19 km or mg < 3.46 × 10 −29 eV. This is the first proof of principles demonstration of setting a limit on the graviton mass using a sample of related galaxy clusters with X-ray measurements and can be easily applied to upcoming X-ray surveys such as eRosita.

Motivated by previous studies about the potential importance of relativistic corrections to galaxy cluster hydrostatic masses, we calculate the masses of 12 relaxed clusters (with Chandra X-ray data) using the Tolman-Oppenheimer-Volkov (TOV) equation of hydrostatic equilibrium and the ideal gas equation of state. Analytical formulae for gas density and temperature profiles for these clusters, previously derived by Vikhlinin et al [1] were used to obtain these masses. We compare the TOV-based masses with those obtained using the corresponding Newtonian equation of hydrostatic equilibrium. We find that the fractional relative difference between the two masses are negligible, corresponding to ∼ O(10 −5 ).

Although galaxy clusters have proved to be wonderful laboratories for testing a plethora of modified gravity theories and other exotic alternatives to ΛCDM, until a few years ago, there was only one paper (from 1974), which obtained a limit on graviton mass (of O(10 −29 ) eV) with clusters. To rectify this, in the last few years multiple works have obtained different bounds on graviton mass using single cluster data as well as stacking galaxy catalogs. We review these recent limits on graviton mass using galaxy clusters obtained using disparate methods.