Cosmic dissonance: new physics or systematics behind a short sound horizon?

Persistent tension between low-redshift observations and the Cosmic Microwave Background radiation (CMB), in terms of two fundamental distance scales set by the sound horizon $r_d$ and the Hubble constant $H_0$, suggests new physics beyond the Standard Model or residual systematics. We examine recently updated distance calibrations from Cepheids, gravitational lensing time-delay observations, and the Tip of the Red Giant Branch. Calibrating the Baryon Acoustic Oscillations (BAO) and Type Ia supernovae with combinations of the distance indicators, we obtain a joint and self-consistent measurement of $H_0$ and $r_d$ at low redshift, independent of cosmological models and CMB inference. In an attempt to alleviate the tension between late-time and CMB-based measurements, we consider four extensions of the standard $\Lambda$CDM model. The sound horizon from our different measurements is $r_d=(137\pm3^{stat.}\pm2^{syst.})$~Mpc. Depending on the adopted distance indicators, the $combined$ tension in $H_0$ and $r_d$ ranges between 2.3 and 5.1 $\sigma$. We find that modifications of $\Lambda$CDM that change the physics after recombination fail to solve the problem, for the reason that they only resolve the tension in $H_0$, while the tension in $r_d$ remains unchanged. Pre-recombination extensions (with early dark energy or the effective number of neutrinos $\rm{N}_{\rm{eff}}=3.24 \pm 0.16$) are allowed by the data, unless the calibration from Cepheids is included. Results from time-delay lenses are consistent with those from distance-ladder calibrations and point to a discrepancy between absolute distance scales measured from the CMB (assuming the standard cosmological model) and late-time observations. New proposals to resolve this tension should be examined with respect to reconciling not only the Hubble constant but also the sound horizon derived from the CMB and other cosmological probes.