Constraining the lensing dispersion from the angular clustering of binary black hole mergers

TL;DR

This paper introduces a method to constrain gravitational lensing dispersion using the angular clustering of gravitational wave sources without needing their redshifts, enhancing high-redshift cosmology.

Contribution

It develops a formalism incorporating second-order lensing effects and demonstrates how joint auto- and cross-correlation analyses can break degeneracies, improving lensing dispersion constraints.

Findings

Auto-correlation signal detectable with future experiments.

Lensing dispersion amplitude decreases with increased lensing effects.

Joint analysis reduces degeneracy between lensing dispersion and source bias.

Abstract

Gravitational waves from inspiraling compact binaries provide direct measurements of luminosity distances and serve as a powerful probe of the high-redshift Universe. In addition to their role as standard sirens, they offer an opportunity to constrain small-scale density fluctuations through the dispersion in the distance-redshift relation induced by gravitational lensing. We propose a method to constrain this lensing dispersion without requiring the redshift information by analyzing the angular clustering of gravitational wave sources. Our formalism incorporating second-order lensing effects in the luminosity distance shows that the amplitude of the auto-correlation angular clustering decreases with increasing lensing dispersion. While we show that the auto-correlation signal is detected with sufficient signal-to-noise ratios in future gravitational wave experiments, there exists a strong degeneracy between the lensing dispersion and the linear bias of gravitational wave sources. We demonstrate that this degeneracy is partially broken by a joint analysis of the auto-correlation of gravitational wave sources and the cross-correlation with galaxies whose redshifts are known. This approach enhances the use of gravitational waves as a cosmological probe at high redshifts.