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.
