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Abstract In this paper, we carry out an assessment of cosmic distance duality relation (CDDR) based on the latest observations of HII galaxies acting as standard candles and ultra-compact structure in radio quasars acting as standard rulers. Particularly, two machine learning reconstruction methods [Gaussian Process (GP) and Artificial Neural Network (ANN)] are applied to reconstruct the Hubble diagrams from observational data. We show that both approaches are capable of reconstructing the current constraints on possible deviations from the CDDR in the redshift range $$z\sim 2.3$$ z ∼ 2.3 . Considering four different parametric methods of CDDR, which quantify deviations from the CDDR and the standard cosmological model, we compare the results of the two different machine learning approaches. It is observed that the validity of CDDR is in well agreement with the current observational data within $$1\sigma $$ 1 σ based on the reconstructed distances through GP in the overlapping redshift domain. Moreover, we find that ultra-compact radio quasars could provide $$10^{-3}$$ 10 - 3 -level constraints on the violation parameter at high redshifts, when combined with the observations of HII galaxies. In the framework of ANN, one could derive robust constraints on the violation parameter at a precision of $$10^{-2}$$ 10 - 2 , with the validity of such distance duality relation within $$2\sigma $$ 2 σ confidence level.

Abstract Direct measurements of Hubble parameters H(z) are very useful for cosmological model parameters inference. Based on them, Sahni, Shafieloo and Starobinski introduced a two-point diagnostic $$Omh^2(z_i, z_j)$$ Omh2(zi,zj) as an interesting tool for testing the validity of the $$\Lambda \hbox {CDM}$$ ΛCDM model. Applying this test they found a tension between observations and predictions of the $$\Lambda \hbox {CDM}$$ ΛCDM model. We use the most comprehensive compilation H(z) data from baryon acoustic oscillations (BAO) and differential ages (DA) of passively evolving galaxies to study cosmological models using the Hubble parameters itself and to distinguish whether $$\Lambda \hbox {CDM}$$ ΛCDM model is consistent with the observational data with statistical analysis of the corresponding $$Omh^2(z_i, z_j)$$ Omh2(zi,zj) two-point diagnostics. Our results show that presently available H(z) data significantly improve the constraints on cosmological parameters. The corresponding statistical $$Omh^2(z_i, z_j)$$ Omh2(zi,zj) two-point diagnostics seems to prefer the quintessence with $$w>-1$$ w>-1 over the $$\Lambda \hbox {CDM}$$ ΛCDM model. Better and more accurate prior knowledge of the Hubble constant, will considerably improve the performance of the statistical $$Omh^2(z_i, z_j)$$ Omh2(zi,zj) method.