Modified Gravity and the Black Hole Mass Gap

Abstract: We pioneer the black hole mass gap as a powerful new tool for constraining modified gravity theories. These theories predict fifth forces that alter the structure and evolution of population-III stars, exacerbating the pair-instability. This results in the formation of lighter astrophysical black holes and lowers both the upper and lower edges of the mass gap. These effects are explored using detailed numerical simulations to derive quantitative predictions that can be used as theoretical inputs for Bayesian data analysis. We discuss detection strategies in light of current and upcoming data as well as complications that may arise due to environmental screening. To demonstrate the constraining power of the mass gap, we present a novel test of the strong equivalence principle where we apply our results to an analysis of the first ten LIGO/Virgo binary black hole merger events to obtain a $7\%$ bound on the relative difference between the gravitational constant experienced by baryonic matter, and that experienced by black holes, $\Delta G/G$. The recent GW190521 event resulting from two black holes with masses in the canonical mass gap can be explained by modified gravity if the event originated from an unscreened galaxy where the strength of gravity is enhanced by $\sim30\%$ or reduced by $\sim 50\%$ relative to its strength in the solar system.