Comparing the Detectability of the Baryon Acoustic Oscillation through Gravitational-Wave Autocorrelation and Cross-Correlation with Galaxies

The amplitude and waveform shape of gravitational wave radiation from compact binary mergers enable a direct measurement of the luminosity distance to these events, making them``standard sirens''. Binary black hole (BBH) mergers form a significant fraction of these standard sirens. A substantial catalog of BBH merger events can be used to probe cosmology and large-scale structure properties, such as the baryon acoustic oscillations (BAO). In this work, we explore detecting the BAO scale using the cross-correlation between BBH mergers and a galaxy catalog, and compare it with the BBH autocorrelation for the third-generation detector observations. Over a 10-year observation period, these observatories will localize approximately 1.5 times10 5 events within 10 square degrees, with at least 50 and luminosity distance uncertainty at most 50 Mpc, and will allow recovery of the BAO scale. We find that the BAO scale is recovered with approximately two times the and a significantly better precision through cross-correlation as compared to autocorrelation.