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We test the possibility that the black holes (BHs) detected byLIGO-Virgo-KAGRA (LVK) may be cosmologically coupled and grow in massproportionally to the cosmological scale factor to some power $k$, which mayalso act as the dark energy source if $k\approx 3$. This approach was proposedas an extension of Kerr BHs embedded in cosmological backgrounds and possiblywithout singularities or horizons. In our analysis, we develop and apply twomethods to test these cosmologically coupled BHs (CCBHs) either with or withoutconnection to dark energy. We consider different scenarios for the time betweenthe binary BH formation and its merger, and we find that the standardlog-uniform distribution yields weaker constraints than the CCBH-correctedcase. 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 observedones had an initial mass below this threshold. We obtain these probabilitieseither directly from the observed data or by assuming the LVKpower-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 thedirect method. Considering the uncertainties on the nature of CCBHs, we alsofind 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 showthat future observations have the potential to decisively confirm these bounds.

Constraints on cosmologically coupled black holes from gravitational wave observations and minimal formation mass