SIMBAD references

The Hubble tension has become one of the central problems in cosmology. In this work, we determine the Hubble constant H₀ and sound horizon r_d by using the combination of baryon acoustic oscillations (BAOs) from DESI surveys, time-delay lensed quasars from H0LiCOW collaborations, and the Pantheon supernova (SN) observations. We consider two cosmological approaches, i.e., Taylor series and Padé polynomials, to avoid cosmological dependence. The reason for using this combination of data is that the absolute distance provided by strong gravitational lensing helps anchor the relative distance of BAOs, and SNe provide a robust history of Universe evolution. Combining the six time-delay distance (6D_Δt) plus four angular diameter distance to the deflector (4D_d) measurements of time-delay lensed quasars, the BAOs, and the Type Ia SN data sets, we obtain a model-independent result of ${r}_{d}=138.{2}_{-3.9}^{+3.3}$ Mpc and ${H}_{0}=72.{9}_{-1.8}^{+1.8}\,\,{\rm{km}}\,{{\rm{s}}}^{-1}\,{{\rm{Mpc}}}^{-1}$ for the Taylor series cosmography and ${r}_{d}=137.{0}_{-3.7}^{+3.2}$ Mpc and ${H}_{0}=73.{1}_{-1.7}^{+1.8}\,\,{\rm{km}}\,{{\rm{s}}}^{-1}\,{{\rm{Mpc}}}^{-1}$ for the Padé polynomial cosmography. The determination of r_d and H₀ prefers larger H₀ and smaller r_d than Planck data under the assumption of a flat Lambda cold dark matter model. However, the values of H₀ are consistent with the H₀ determination from the SH0ES collaboration.