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The recent local measurements of the Hubble constant $H_0$, indicate asignificant discrepancy of over 5$\sigma$ compared to the value inferred from\textit{Planck} observations of the cosmic microwave background (CMB). In thispaper, we try to understand the origin of this tension by testing theconsistency of early and late cosmological parameters in the same observeddata. In practice, we simultaneously derive the early and late parameters usingbaryon acoustic oscillation (BAO) measurements, which provide both low andhigh-redshift information. To resolve parameter degeneracy, the complementarydata from CMB observations are included in the analysis. By using the parameter$\omega_m = \Omega_mh^2$, we introduce ${\rm ratio}(\omega_m)$, defined as theratio of $\omega_m$ which are constrained from high and low-redshiftmeasurements respectively, to quantify the consistency between early and lateparameters. We obtained a value of ${\rm ratio}(\omega_m) = 1.0069\pm0.0070$,indicating there is no tension between early parameters and late parameters inthe framework of $\Lambda$CDM model. As a result, the Hubble tension may arisefrom the differences of datasets or unknown systematic errors in the currentdata. In addition, we forecast the future BAO measurements of ${\rmratio}(\omega_m)$, using several galaxy redshift surveys and 21 cm intensitymapping surveys, and find that these measurements can significantly improve theprecision of cosmological parameters.

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