Constraints on the Cosmological Coupling of Black Holes from the Globular Cluster NGC 3201

Globular clusters are among the oldest stellar populations in the Milky Way; consequently, they also host some of the oldest known stellar-mass black holes, providing insight into black hole formation and evolution in the early ($z\gtrsim 2$) Universe. Recent observations of supermassive black holes in elliptical galaxies have been invoked to suggest the possibility of a cosmological coupling between astrophysical black holes and the surrounding expanding Universe, offering a mechanism for black holes to grow over cosmic time, and potentially explaining the origin of dark energy. In this paper, I show that the mass functions of the two radial velocity black hole candidates in NGC 3201 place strong constraints on the cosmologically-coupled growth of black holes. In particular, the amount of coupling required to explain the origin of dark energy would either require both NGC 3201 black holes to be nearly face on (a configuration with probability of at most $10^{-4}$) or one of the BHs would need to have formed with a mass below that of the most massive neutron stars ($2.2M_{\odot}$). This emphasizes that these and other detached black hole-star binaries can serve not only as laboratories for compact object and binary astrophysics, but as constraints on the long-term evolution of astrophysical black holes.