  The gravitational wave (GW) signal from the merger of two black holes can
serve as a standard sirens for cosmological inference. However, a degeneracy
exists between the luminosity distance and the inclination angle between the
binary system's orbital angular momentum and the observer's line of sight,
limiting the precise measurement of the luminosity distance. In this study, we
investigate how higher harmonics affect luminosity distance estimation for
third-generation (3G) GW detectors in binary black hole mergers. Our findings
demonstrate that considering higher harmonics significantly enhances distance
inference results compared with using only the (2,2) mode. This improved
accuracy in distance estimates also strengthens constraints on host galaxies,
enabling more precise measurements of the Hubble constant. These results
highlight the significant influence of higher harmonics on the range estimation
accuracy of 3G ground-based GW detectors.
