High-redshift cosmography: Application and comparison with different methods

Abstract

Cosmography is used in cosmological data processing in order to constrain the kinematics of the universe in a model-independent way. In this paper, we first investigate the effect of the ultraviolet (UV) and X-ray relation of a quasar on cosmological constraints. By fitting the quasar relation and cosmographic parameters simultaneously, we find that the 4I deviation from the cosmological constant I cold dark matter (I CDM) model disappears. Next, utilizing the Pantheon sample and 31 long gamma-ray bursts, we make a comparison among the different cosmographic expansions (z-redshift, y-redshift, E(y), log(1a +a z), log(1a +a z)+kij, and Padé approximations) with the third-order and fourth-order expansions. The expansion order can significantly affect the results, especially for the y-redshift method. Through analysis from the same sample, the lower-order expansion is preferable, except the y-redshift and E(y) methods. For the y-redshift and E(y) methods, despite adopting the same parameterization of ya =a z/(1a +a z), the performance of the latter is better than that of the former. Logarithmic polynomials, log(1a +a z) and log(1a +a z)+kij, perform significantly better than z-redshift, y-redshift, and E(y) methods, but worse than Padé approximations. Finally, we comprehensively analyze the results obtained from different samples. We find that the Pade(2,1) method is suitable for both low and high redshift cases. The Pade(2,2) method performs well in a high-redshift situation. For the y-redshift and E(y) methods, the only constraint on the first two parameters (q0 and j0) is reliable.