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 4$\sigma$ deviation from the cosmological constant cold dark matter ($\Lambda$CDM) model disappears. Next, utilizing the Pantheon sample and 31 long gamma-ray bursts (LGRBs), we make a comparison among the different cosmographic expansions ($z$-redshift, $y$-redshift, $E(y)$, $\log (1+z)$, $\log (1+z)+k_{ij}$, and Pad$\acute{\mathrm{e}}$ 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 Pad$\acute{\mathrm{e}}$ approximations. Finally, we comprehensively analyze the results obtained from different samples. We find that the Pad${\acute{\mathrm{e}}}_{(2,1)}$ method is suitable for both low and high redshift cases. The Pad${\acute{\mathrm{e}}}_{(2,2)}$ method performs well in a high-redshift situation. For the $y$-redshift and $E(y)$ methods, the only constraint on the first two parameters ($q_0$ and $j_0$) is reliable.

arXiv comment15 pages, 12 figures, accepted for publication in A&A

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