Improvement of graviton mass constraints using GRAVITY's detection of Schwarzschild precession in the orbit of S2 star around the Galactic Center

Abstract

Here we study the possible improvements of the existing constraints on the upper bound of graviton mass by the analysis of the stellar orbits around the supermassive black hole (SMBH) at the Galactic Center (GC) in the framework of Yukawa gravity. Main motivation for this study is recent detection of Schwarzschild precession in the orbit of S2 star around the SMBH at the GC by the GRAVITY Collaboration in 2020. They indicated that the orbital precession of the S2 star is close to the General Relativity (GR) prediction, but with possible small deviation from it, and parametrized this effect by introducing an ad hoc factor in the parameterized post-Newtonian (PPN) equations of motion. Here we use the value of this factor presented by GRAVITY in order to perform two-body simulations of the stellar orbits in massive gravity using equations of motion in the modified PPN formalism, as well as to constrain the range of massive interaction $\Lambda$. From the obtained values of $\Lambda$, and assuming that it corresponds to the Compton wavelength of graviton, we then calculated new estimates for the upper bound of graviton mass which are found to be independent, but consistent with the LIGO's estimate of graviton mass from the first gravitational wave (GW) signal GW150914. We also performed Markov chain Monte Carlo (MCMC) simulations in order to constrain the bounds on graviton mass in the case of a small deviation of the stellar orbits from the corresponding GR predictions and showed that our method could further improve previous estimates for upper bounds on the graviton mass. It is also demonstrated that such analysis of the observed orbits of S-stars around the GC in the frame of the Yukawa gravity represents a tool for constraining the upper bound for the graviton mass, as well as for probing the predictions of GR or other gravity theories.Comment: 13 pages, 2 tables, 6 figure