A model-independent determination of the sound horizon using recent BAO measurements and strong lensing systems

We propose an improved method to determine the sound horizon in a cosmological model-independent way by using the latest observations of BAO measurements from DES, BOSS/eBOSS, and DESI surveys and gravitationally time-delay lensed quasars from H0LiCOW collaboration. Combining the 6$D_{\Delta t}$ plus 4$D_{d}$ measurements and the reconstructed BAO datasets, we obtain a model-independent result of $r_d=139.7^{+5.2}_{-4.5}$ Mpc, with the precision at the $\sim3.7\%$ level, which is in agreement with the result of Planck 2018 within $\sim1.7\sigma$ uncertainty. Our method is independent of cosmological parameters such as the Hubble constant, dark energy, (and, more importantly, does not involve the cosmic curvature when using the $D_d$ measurements of the lenses, and also avoids the obstacle of mass-sheet degeneracy in gravitational lensing). Meanwhile, it does not need to consider the Eddington relation with concerning the transformation of distance. Since only two types of data are considered, the contribution of each can be clearly understood. Our results also highlight the Hubble tension and may give us a better understanding of the discordance between the datasets or reveal new physics beyond the standard model.