Context. 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 rd and the Hubble constant H0, suggests new physics beyond the Standard Model, departures from concordance cosmology, or residual systematics.
Aims. The role of different probe combinations must be assessed, as well as of different physical models that can alter the expansion history of the Universe and the inferred cosmological parameters.
Methods. We examined recently updated distance calibrations from Cepheids, gravitational lensing time-delay observations, and the tip of the red giant branch. Calibrating the baryon acoustic oscillations and type Ia supernovae with combinations of the distance indicators, we obtained a joint and self-consistent measurement of H0 and rd 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 considered four extensions of the standard ΛCDM model.
Results. The sound horizon from our different measurements is rd = (137 ± 3stat. ± 2syst.) Mpc based on absolute distance calibration from gravitational lensing and the cosmic distance ladder. Depending on the adopted distance indicators, the combined tension in H0 and rd ranges between 2.3 and 5.1 σ, and it is independent of changes to the low-redshift expansion history. We find that modifications of ΛCDM that change the physics after recombination fail to provide a solution to the problem, for the reason that they only resolve the tension in H0, while the tension in rd remains unchanged. Pre-recombination extensions (with early dark energy or the effective number of neutrinos Neff = 3.24 ± 0.16) are allowed by the data, unless the calibration from Cepheids is included.
Conclusions. 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.
Low-redshift measurement of the sound horizon through gravitational time-delays