Abstract
The Cosmic Microwave Background (CMB) yields an inference on the matter sound
horizon, within the Standard Model. Independent, direct measurements of the
sound horizon are then a probe of possible deviations from the Standard Model.
We aim at measuring the sound horizon $r_s$ from low-redshift indicators,
completely independent from CMB inference. We use the measured product
$H(z)r_s$ from Baryon Acoustic Oscillations (BAO), plus Supernovae~Ia
to constrain $H(z)/H_0$ and time-delay lenses analysed by the H0LiCOW
collaboration to anchor cosmological distances ($H_0^-1$).
Additionally, we investigate the influence of adding a sample of
higher-redshift quasars with standardisable UV-Xray luminosity distances. We
adopt polynomial expansions in $H(z)$ or in comoving distances, so that our
inference is completely independent of any underlying cosmological model. Our
measurements are independent of Cepheids and systematics from peculiar motions,
to within percent-level accuracy. The inferred sound horizon $r_s$ varies
between $(133 8)$~Mpc and $(138 5)$~Mpc across different models. The
discrepancy with CMB measurements is robust against model choice. Statistical
uncertainties are comparable to systematics. The combination of time-delay
lenses, supernovae and BAO yields a cosmology-independent (and
Cepheid-calibration-independent) distance ladder, and a CMB-independent
measurement of $r_s.$ These cosmographic measurements are then a competitive
test of the Standard Model, regardless of hypotheses on the underlying
cosmology.
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