Can cosmologically-coupled mass growth of black holes solve the mass gap problem?

Observations of elliptical galaxies suggest that black holes (BHs) might serve as dark energy candidates, coupled to the expansion of the Universe. According to this hypothesis, the mass of a BH could increase as the Universe expands. BH low-mass X-ray binaries (LMXBs) in the Galactic disk were born several gigayears ago, making the coupling effect potentially significant. In this work, we calculate the evolution of BH binaries with a binary population synthesis method to examine the possible influence of cosmologically-coupled growth of BHs, if it really exists. The measured masses of the compact objects in LMXBs show a gap around $\sim 2.5-5~{\rm M_\odot}$, separating the most massive neutron stars from the least massive BHs. Our calculated results indicate that, considering the mass growth seem to (partially) account for the mass gap and the formation of compact BH LMXBs, alleviating the challenges in modeling the formation and evolution of BH LMXBs with traditional theory. However, critical observational evidence like the detection of intermediate-mass black hole binaries is required to test this hypothesis.