Can high-redshift Hubble diagrams rule out the standard model of cosmology in the context of cosmographic method?

Abstract: Using mock data for the Hubble diagrams of type Ia supernovae (SNIa) and quasars (QSOs) generated based on the standard model of cosmology, and using the least-squares method based on the Markov-Chain-Monte-Carlo (MCMC) algorithm, we first put constraints on the cosmographic parameters in the context of the various model-independent cosmographic methods reconstructed from the Taylor $4^{th}$ and $5^{th}$ order expansions and the Pade (2,2) and (3,2) polynomials of the Hubble parameter, respectively. We then reconstruct the distance modulus in the framework of cosmographic methods and calculate the percentage difference between the distance modulus of the cosmographic methods and that of the standard model. The percentage difference is minimized when the Pade approximation is used which means that the Pade cosmographic method is sufficiently suitable for reconstructing the distance modulus even at high-redshifts. In the next step, using the real observational data for the Hubble diagrams of SNIa, QSOs, gamma-ray-bursts (GRBs), and observations from baryon acoustic oscillations (BAO) in two sets of the low-redshift combination (SNIa+QSOs+GRBs+BAO) embracing the redshift range of $0.01<z<2.26$ and the high-redshift combination (SNIa+QSOs+GRBs) which covers a redshift range of $0.01< z < 5.5$, we put observational constraints on the cosmographic parameters of the Pade cosmography and also the standard model. Our analysis indicates that Pade cosmographic approaches do not reveal any cosmographic tension between the standard model and the observational data. We also confirm this result, using the statistical AIC criteria. Finally, we put the cosmographic method in the redshift-bin data and find a larger value of $\Omega_{m0}$ extracted from $s_0$ parameter compared with those of the $q_0$ parameter and Planck-$\Lambda$CDM values.