Constraints on sound horizon r_d, Hubble constant H₀ and Ω_k from late-time observations including BAO (BOSS), type Ia supernovae (Pantheon), gravitational lensing (H0LiCOW) and cosmic distance ladder calibrated with Cepheids (SH0ES). The panels show results for three cosmology-independent models listed in Table 1 and a ΛCDM cosmological model. The red lines indicate the best fit values obtained from Planck for a flat ΛCDM cosmological model. The contours indicate 1-, 2- and 5σ confidence regions of the posterior probability (the latter obtained by Gaussian extrapolation). All panels demonstrate a 5σ tension between r_d and H₀ measured from the CMB and the late-time observations.