High-redshift cosmography: Application and comparison with different methods

TL;DR

This study compares various cosmographic methods using quasar, supernova, and gamma-ray burst data, revealing the impact of expansion choice on cosmological constraints and identifying the most effective approaches for different redshift ranges.

Contribution

It systematically evaluates multiple cosmographic expansions and their performance across different datasets, highlighting the advantages of logarithmic polynomials and Padé approximations.

Findings

Logarithmic polynomials outperform some traditional methods.

Padé approximations are effective for both low and high redshift data.

Lower-order expansions are generally preferable, except for specific 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$\rm \acute{e}$ 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$\rm \acute{e}$ approximations. Finally, we comprehensively analyze the results obtained from different samples. We find that the Pad$\rm \acute{e}_{(2,1)}$ method is suitable for both low and high redshift cases. The Pad$\rm \acute{e}_{(2,2)}$ 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.