AI 中文总结
本文提出适用于4维洛伦兹时空的任意红移中心一般宇宙学展开式，通过LTB度规案例检验其重现红移-距离关系的能力，探讨了用该展开式约束宇宙学量的策略。
AI 中文摘要
随着即将开展的巡天项目提供大量覆盖宽红移范围的高精度观测数据，开发无需预设宇宙学模型即可将观测数据转化为几何与动力学信息的工具愈发重要。以任意红移为中心的一般宇宙学展开式恰好提供了这类工具。本文提出适用于4维洛伦兹时空的、以任意红移为中心的一般宇宙学展开式的形式体系，随后将该展开形式体系应用于两个由勒梅特-托尔曼-邦迪（Lemaître-Tolman-Bondi）度规模型的大尺度宇宙结构（低密度区与高密度区）案例中，检验其重现红移-距离关系的能力，同时考察为宇宙学级数展开选择不同红移区间的影响。这一工作量化了从红移-距离观测中推断出的宇宙学系数在多大程度上可保留其作为局域几何与动力学量的解释（正如标准FLRW宇宙学所预期的那样）。与早期结果类似，本文发现，在更一般的时空中，这些系数会成为反映所探测有限观测范围的有效参数。最后，本文探讨了利用该展开式约束动力学与几何量的可能策略。
英文摘要
With upcoming surveys providing large volumes of highly precise observational data across a wide range of redshifts, it is increasingly important to have tools that can translate observational data into geometric and dynamical information without imposing a predetermined cosmological model. General cosmographic expansions centred at arbitrary redshift provide exactly such a tool. We here present the formalism for general cosmographic expansions centred at an arbitrary redshift, valid for 4-dimensional Lorentzian spacetimes. We then apply the expansion formalism to test its ability to reproduce the redshift-distance relation in two examples of large-scale cosmic structures (an underdensity and an overdensity) modelled by the Lemaître-Tolman-Bondi metric, where we examine the effect of choosing different redshift intervals for the cosmographic series expansions. This quantifies the extent to which cosmographic coefficients inferred from redshift-distance observations retain their interpretation as local geometric and dynamical quantities, as is expected in standard FLRW cosmology. Similarly to earlier results, we here find that in more general spacetimes the coefficients instead become effective parameters reflecting the finite observational range probed. Lastly, we discuss possible strategies for using the expansions to constrain dynamical and geometric quantities.
Comments15 pages, 10 captioned figures. Prepared for submission to the Open Journal of Astrophysics
