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tokens: data. Results from this joint analysis are listed in Tables 1 , 2 , and 6 . The QSO + H ( z ) + BAO 1D likelihoods and 2D confidence contours for all free parameters are shown in blue in Figs 4 – 15 . The updated QSO data don’t significantly tighten the BAO + H ( z ) data contours except in the cases of the non-flat XCDM parametrization and the non-flat φCDM model (Figs 10 , 11 , 14 , and 15 ). Another noticeable result is that adding the QSO data to the BAO + H ( z ) data results in the shifting of 1D likelihood distribution of the matter density parameter towards higher values in most cosmological models studied here. Table 5. Marginalized 1D best-fitting parameters with 1σ confidence intervals for all models using BAO and H ( z ) data (from Khadka Ratra 2020 ). a . From joint analyses of the QSO + H ( z ) + BAO data, from Table 6 , the matter density parameter lies in the range Ω m 0 = 0.30 ± 0.02 to 0.31 ± 0.01 (Ω m 0 = 0.30 ± 0.01 to 0.33 ± 0.02) for flat (non-flat) models and the H 0 = 68 ± 2.8 prior and lies in the range Ω m 0 = to 0.31 ± 0.01 (Ω m 0 = 0.31 ± 0.01 to 0.33 ± 0.02) for flat (non-flat) models and the H 0 = 73.24 ± 1.74 prior. In a few cases these results slightly differ from the BAO + H ( z ) data results in Table 5 , being shifted to slightly larger values. These results are consistent with those results determined from other cosmological data. Table 6. Marginalized 1D best-fitting parameters with 1σ confidence intervals for all models using QSO + H ( z ) + BAO data. a . The Hubble constant lies in the range H 0 = to ( H 0 = to ) for flat (non-flat) models and the H 0 = 68 ± 2.8 prior and lies in the range H 0 = to ( H 0 = to ) for flat (non-flat) models and the H 0 = 73.24 ± 1.74 prior. Not unexpectedly, for the H 0 = 73.24 ± 1.74 prior case the measured value of H 0 is reduced below the prior value because the BAO and H ( z ) observations prefer a lower H 0 . In most cases the H 0 error bars have increased in comparison to those derived using the 2015 QSO + BAO + H ( z ) data in Khadka Ratra ( 2020 ). In all models, except for non-flat ΛCDM with the H 0 = 68 ± 2.8 prior, closed spatial hypersurfaces are favoured at about 2σ. For the non-flat ΛCDM model the curvature energy density parameter is Ω k 0 = and −0.09 ± 0.05 for the H 0 = 68 ± 2.8 and 73.24 ± 1.74 priors, respectively. Values of curvature energy density parameter obtained for non-flat dynamical dark energy cosmological models are significantly higher than those obtained in the non-flat ΛCDM model. The curvature energy density parameter is Ω k 0 = −0.34 ± 0.18 and −0.32 ± 0.16 for the non-flat XCDM and non-flat φCDM models for the H 0 = 68 ± 2.8 prior and Ω k 0 = and −0.35 ± 0.15 for the non-flat XCDM and non-flat φCDM models for the H 0 = 73.24 ± 1.74 prior. This preference for closed spatial geometries is largely driven by the BAO + H ( z ) data (Park Ratra 2018c ; Ryan et al. 2019 ). From Table 6 , for the flat (non-flat) ΛCDM model the dark energy density