Abstract:
This thesis presents a framework to quantify the clustering of gravitational wave (GW) transient sources and measure their spatial cross-correlation with the large-scale structure of the universe using k-nearest neighbour (kNN) distributions and two-point summary statistics. We extend the kNN formalism, initially developed to study 3D clustering in cartesian coordinates, to 2D clustering in angular coordinates. As a first application to data, we measure the nearest-neighbour distributions of 53 suitably selected Binary Black Hole (BBH) mergers detected in the first three observation runs of LIGO-Virgo-KAGRA and cross-correlate these sources with ∼1.7×10^7 galaxies and quasars from the WISE×SuperCOSMOS all-sky catalogue. To determine the significance of the clustering signal while accounting for observational systematics in the GW data, we create 135 realisations of mock BBHs that are statistically similar to the observed BBHs but spatially unclustered. We find no evidence for spatial clustering or cross-correlation with large-scale structure in the data and conclude that the present sky localisation and number of detections are insufficient to get a statistically significant clustering signal. As a second application of our analysis framework, we investigate the feasibility of detecting the BBH-galaxy cross-correlation with future GW observing runs and stage-IV large-scale structure surveys. We forecast 10 years of GW observations with a network of 5 ground-based detectors consisting of 3 advanced LIGO detectors (Hanford, Livingston, India) operating at A+ sensitivity and Virgo, KAGRA operating at design sensitivity. The resulting BBH catalogue consists of ∼2.8 × 10^4 BBHs, of which ∼1.6 × 10^4 have a 68% credible sky localisation area less than 50 sq. deg. We cross-correlate these modestly well-localised BBHs with the simulated galaxy overdensity field of an LSST Y1-like survey and find that the second nearest neighbour distribution captures a nearly statistically significant cross-correlation signal at ∼1 deg. angular scales. We further show that this signal is not measured by the two-point cross-correlation function, demonstrating the ability of the nearest neighbour distributions to extract higher-order, non-Gaussian clustering from the small spatial scales accessible with upcoming GW observations and large-scale surveys that makes them more robust measures of spatial clustering than two-point clustering statistics that capture only the Gaussian clustering on all scales.
