arXiv 2202.090752022-02-18astro-ph.COastro-ph.HE

高红移宇宙照相术：不同方法的应用和比较

High-redshift cosmography: Application and comparison with different methods

J. P. Hu, F. Y. Wang

备注：: 15 pages, 12 figures, accepted for publication in A&A
发表信息：: A&A 661, A71 (2022)
DOI：: 10.1051/0004-6361/202142162

摘要：

宇宙学被用于宇宙学数据处理，以便以独立于模型的方式约束宇宙的运动学。本文首先研究了类星体的紫外和X射线关系对宇宙学约束的影响。通过同时拟合类星体关系和宇宙学参数，我们发现$Λ$模型与宇宙学常数冷暗物质（$Λ$ CDM）模型的4个偏差消失了。其次，利用Pantheon样品和31个长伽玛射线暴（LGRB），我们比较了不同的宇宙学展开（$z$ -红移，$y$ -红移，$E(y)$，$\log(1+z)$，$\log(1+z)+k_{ij}$和Pad $\rm \acute{e}$近似）与三阶和四阶展开。展开阶数对结果有很大的影响，特别是对于$y$ -红移方法.通过对同一样品的分析，除$y$ -红移和$E(y)$方法外，低阶展开法更可取。对于$y$ -红移和$E(y)$方法，尽管采用了与$y=z/(1+z)$相同的参数化，但后者的性能优于前者。对数多项式$\log(1+z)$和$\log(1+z) + k_{ij}$的性能明显优于$z$ -红移、$y$ -红移和$E(y)$方法，但不如Pad $\rm \acute{e}$近似。最后，我们综合分析了不同样本的结果。我们发现，垫$\rm \acute{e}_{(2,1)}$方法是适用于低和高红移的情况。Pad $\rm \acute{e}_{(2,2)}$方法在高红移情况下表现良好。对于$y$ -红移和$E(y)$方法，只有对前两个参数（$q_{0}$和$j_{0}$）的约束是可靠的.

英文摘要：

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$σ$ deviation from the cosmological constant cold dark matter ($Λ$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.

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