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

TL;DR

This paper investigates whether black holes observed by gravitational wave detectors could be cosmologically coupled, growing in mass with the universe's expansion, and derives constraints on this hypothesis using current data.

Contribution

The study develops two methods to test cosmologically coupled black holes and provides the first constraints on the coupling parameter k from gravitational wave observations.

Findings

For k<2.1 (standard distribution), the coupling hypothesis is constrained at 2σ.

The minimum initial mass for black holes to avoid tension with observations is below 0.5 M_sun.

Future gravitational wave data can further tighten these bounds.

Abstract

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.