Testing the consistency of early and late cosmological parameters with BAO and CMB data

The recent local measurements of the Hubble constant H0, indicate a significant discrepancy of over 5σ compared to the value inferred from Planck observations of the cosmic microwave background (CMB). In this paper, we try to test the standard cosmological model ΛCDM by testing the consistency of early and late cosmological parameters in the same observed data. In practice, we simultaneously derive the early and late parameters using baryon acoustic oscillation (BAO) measurements, which provide both low and high-redshift information. CMB data are also included in the analysis as a "distance prior", which tracks the same BAO feature and resolve parameter degeneracy. By using the parameter ωm=Ωmh2, we introduce ratio(ωm), defined as the ratio of ωm which are constrained from high and low-redshift measurements respectively, to quantify the consistency between early and late parameters. We obtained a value of ratio(ωm)=1.0069±0.0070, indicating there is no tension between early parameters and late parameters in the framework of ΛCDM model. As a result, our test does not expose the defects of the ΛCDM model. In addition, we forecast the future BAO measurements of ratio(ωm), using several galaxy redshift surveys and 21 cm intensity mapping surveys, and find that these measurements can significantly improve the precision of cosmological parameters.