Bounds on $Λ$ at the Galactic Center

Abstract

We constrain the cosmological constant, $Λ$, using astrometric and spectroscopic observations of the S2 star, supplemented by S1 and S14 stars orbiting Sgr A$^*$. We develop a framework for modelling relativistic stellar orbits in general spherically symmetric spacetimes and perform Bayesian parameter estimation to jointly infer orbital and spacetime parameters. Applying this framework to Schwarzschild-de Sitter spacetime, we obtain upper bounds on $Λ$. The individual constraints exhibit the expected dependence on the dynamical timescales of the stars, with the longer-period S1 providing the strongest sensitivity. Combining the individual constraints, we obtain $Λ\lesssim 6.9\times10^{-48}\mathrm{m}^{-2}$ at 68\% credibility and $Λ\lesssim 1.0\times10^{-38}\mathrm{m}^{-2}$ at 95\% credibility. The 68\% constraint is the strongest bound at a comparable dynamical timescale.