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 $\mathit{\text{“standard}}\mathit{\text{sirens”}}$. 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 $1.5\times {10}^5$ events within $10$ square degrees, with \snr $\ge 50$ and luminosity distance uncertainty $\le 50$ Mpc, and will allow recovery of the BAO scale. We find that the BAO scale is recovered with approximately two times the \snr and a significantly better precision through cross-correlation as compared to autocorrelation.