Bounds on $\hat{I}›$ at the Galactic Center

Abstract

We constrain the cosmological constant $\hat{I}›$ using astrometric and spectroscopic observations of the S2, S1, and S14 stars orbiting Sgr A${}^{\ast }$. The stellar motion is modelled by numerically integrating timelike geodesics in Schwarzschild-de Sitter spacetime, including relativistic redshift and time-delay corrections. Orbital and spacetime parameters are inferred using a Bayesian MCMC analysis. The resulting posterior distributions place upper bounds on the magnitude of $\hat{I}›$ at the Galactic Center (GC). Combining the independent constraints from the S2, S1, and S14 orbits yields upper bounds of $\hat{I}›\lesssim 6.9\times 10^{-48}{\mathrm{m}}^{-2}$ at 68\% credibility and $\hat{I}›\lesssim 1.0\times 10^{-38}{\mathrm{m}}^{-2}$ at 95\% credibility.

28 pages, 9 figures