Gravitational waves (GW) from the inspiral of binary compact objects offers a
one-step measurement of the luminosity distance to the event, which is
essential for the measurement of the Hubble constant, $H_0$, that characterizes
the expansion rate of the Universe. However, unlike binary neutron stars, the
inspiral of binary black holes is not expected to be accompanied by
electromagnetic radiation and a subsequent determination of its redshift.
Consequently, independent redshift measurements of such GW events are necessary
to measure $H_0$. In this study, we present a novel Bayesian approach to infer
$H_0$ from the cross-correlation between galaxies with known redshifts and
individual binary black hole merger events. We demonstrate the efficacy of our
method with $250$ simulated GW events distributed within $1$ Gpc in colored
Gaussian noise of Advanced LIGO and Advanced Virgo detectors operating at O4
sensitivity. We show that such measurements can constrain the Hubble constant
with a precision of $lesssim 15 %$ ($90%$ highest density interval). We
highlight the potential improvements that need to be accounted for in further
studies before the method can be applied to real data.
The study discusses the importance of measuring the Hubble constant, which characterizes the expansion rate of the Universe. It highlights that gravitational waves (GW) from the inspiral of binary black holes can provide a measurement of the luminosity distance to the event, but additional redshift measurements are necessary to determine the Hubble constant. The researchers present a Bayesian approach to infer the Hubble constant using the cross-correlation between galaxies with known redshifts and individual binary black hole merger events. They demonstrate the effectiveness of their method using simulated GW events.
To further improve this method and apply it to real data, the researchers outline several potential improvements:
- Increased Sample Size: The study used 250 simulated GW events, but a larger sample size would enhance the precision of the Hubble constant measurement.
- Redshift Measurement Accuracy: Accurate and precise redshift measurements are crucial for determining the Hubble constant. Improvements in redshift estimation techniques could enhance the accuracy of the method.
- Effective Signal Filtering: The researchers used colored Gaussian noise in their simulations. To apply the method to real data, effective signal filtering techniques must be developed to minimize noise and enhance signal detection.
- Detector Sensitivity: The study used data from Advanced LIGO and Advanced Virgo detectors at O4 sensitivity. Future improvements in detector sensitivity would allow for the detection of weaker gravitational wave signals, thereby expanding the sample size and improving measurement precision.
Overall, this study presents a promising Bayesian approach to infer the Hubble constant using cross-correlation between galaxies and binary black hole merger events. Future advancements in sample size, redshift measurement accuracy, signal filtering methods, and detector sensitivity will be instrumental in refining this method and applying it to real data, ultimately providing a more precise measurement of the Hubble constant and deepening our understanding of the expansion rate of the Universe.