High-redshift cosmography: Application and comparison with different methods

¹ School of Astronomy and Space Science, Nanjing University, Nanjing 210093, PR China
e-mail: fayinwang@nju.edu.cn
² Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, PR China

Received: 6 September 2021
Accepted: 15 February 2022

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 4σ deviation from the cosmological constant Λ cold dark matter (ΛCDM) 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(1 + z), log(1 + z)+k_ij, 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 y = z/(1 + z), the performance of the latter is better than that of the former. Logarithmic polynomials, log(1 + z) and log(1 + z)+k_ij, 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 Padé_(2,1) method is suitable for both low and high redshift cases. The Padé_(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.