  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.
