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

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##### Citation

Amendola, L., Rodrigues, D. C., Kumar, S., & Quartin, M. (2024). Constraints on
cosmologically coupled black holes from gravitational wave observations and minimal formation mass.*
Monthly Notices of the Royal Astronomical Society,* *528*(2), 2377-2390. doi:10.1093/mnras/stae143.

Cite as: https://hdl.handle.net/21.11116/0000-000F-195D-E

##### 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.

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.