Abstract
Persistent tension between low-redshift and the Cosmic Microwave Background
(CMB) measurements, in terms of the sound horizon and the Hubble-Lemaître
constant, suggests new physics beyond the Standard Model, departures from
concordance cosmology, or residual systematics. Assessing the likelihood of new
physics devised to resolve the tension requires thorough consistency tests of
several independent and high-precision distance calibrations. We examine recent
updated distance calibrations from Cepheids, gravitational lensing time-delay
observations, and the Tip of the Red Giant Branch. Through selected
cosmographic methods for combining observations of the Baryon Acoustic
Oscillations (BAO), Type Ia supernovae and local distance calibrators, we
obtain robust measurements of the sound horizon, independent of cosmological
models and the CMB. For our different models and probes, the sound horizon
scale varies between $r_s=(135\pm3)$ and $r_s=(140\pm3)$~Mpc. The
combined tension in the sound horizon and the Hubble-Lemaître constant ranges
between $3\sigma$ and $5\sigma$, depending on whether distance ladder
calibrations are used, and is independent of possible changes to the
late-Universe expansion history. Early-Universe extensions with
$N_eff=3.27\pm0.15$ are allowed by the data, unless a
Cepheid distance calibration is included. Some late-dark-energy models, as
constrained by the relative supernova distance moduli, do not resolve the
current tension. Results from time-delay lenses are consistent with those from
distance-ladder calibrations. With upcoming lens samples, the tension in the
inferred sound horizon will be completely independent from local calibrations.
New proposals to resolve the tension should examine CMB and late-Universe
constraints separately, and the inference on both $H_0$ and $r_s.$
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