  We test the possibility that the black holes (BHs) detected by
LIGO-Virgo-KAGRA (LVK) may be cosmologically coupled and grow in mass
proportionally to the cosmological scale factor to some power $k$, which may
also act as the dark energy source if $k\approx 3$. This approach was proposed
as an extension of Kerr BHs embedded in cosmological backgrounds and possibly
without singularities or horizons. In our analysis, we develop and apply two
methods to test these cosmologically coupled BHs (CCBHs) either with or without
connection to dark energy. We consider different scenarios for the time between
the binary BH formation and its merger, and we find that the standard
log-uniform distribution yields weaker constraints than the CCBH-corrected
case. Assuming that the minimum mass of a BH with stellar progenitor is
$2M_\odot$, we estimate the probability that at least one BH among the observed
ones had an initial mass below this threshold. We obtain these probabilities
either directly from the observed data or by assuming the LVK
power-law-plus-peak mass distribution. In the latter case we find, at $2\sigma$
level, that $k < 2.1$ for the standard log-uniform distribution, or $k < 1.1$
for the CCBH-corrected distribution. Slightly weaker bounds are obtained in the
direct method. Considering the uncertainties on the nature of CCBHs, we also
find that the required minimum CCBH mass value to eliminate the tensions for
$k=3$ should be lower than 0.5 $M_\odot$ (again at 2$\sigma$). Finally, we show
that future observations have the potential to decisively confirm these bounds.
