Low-redshift measurement of the sound horizon through gravitational time-delays

Abstract

Context. The matter sound horizon can be infered from the cosmic microwave background within the Standard Model. Independent direct measurements of the sound horizon are then a probe of possible deviations from the Standard Model. Aims. We aim at measuring the sound horizon rs from low-redshift indicators, which are completely independent of CMB inference. Methods. We used the measured product H(z)rs from baryon acoustic oscillations (BAO) together with supernovae Ia to constrain H(z)/H0 and time-delay lenses analysed by the H0LiCOW collaboration to anchor cosmological distances (∝ H0-1). Additionally, we investigated the influence of adding a sample of quasars with higher redshift with standardisable UV-Xray luminosity distances. We adopted polynomial expansions in H(z) or in comoving distances so that our inference was completely independent of any cosmological model on which the expansion history might be based. Our measurements are independent of Cepheids and systematics from peculiar motions to within percent-level accuracy. Results. The inferred sound horizon rs 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. Conclusions. The combination of time-delay lenses, supernovae, and BAO yields a distance ladder that is independent of cosmology (and of Cepheid calibration) and a measurement of rs that is independent of the CMB. These cosmographic measurements are then a competitive test of the Standard Model, regardless of the hypotheses on which the cosmology is based.