[论文解读] Redshift and redshift-drift in $\Lambda = 0$ quasi-spherical Szekeres cosmological models and the effect of averaging

Priti Mishra, Marie-Noëlle Célérier|arXiv (Cornell University)|Mar 20, 2014

Cosmology and Gravitation Theories参考文献 1被引用 3

一句话总结

本文推导了无暗能量的广义准球对称Szekeres（QSS）模型的红移与红移-漂移方程，并将其应用于Bolekjo-Sussman（BSQSS）模型。研究发现，BSQSS模型预测存在宇宙学蓝移——现实中未被观测到——因此被排除；但同时表明，对这类模型进行平均可得到物理上可行的替代ΛCDM模型，且可通过红移-漂移测量加以区分。

ABSTRACT

Since the advent of the accelerated expanding homogeneous universe model, some other explanations for the supernova Ia dimming have been explored, among which there are inhomogeneous models constructed with exact $\Lambda = 0$ solutions of Einstein's equations. They have been used either as one patch or to build Swiss-cheese models. The most studied ones have been the Lema\^itre-Tolman-Bondi (LTB) models. However, these models being spatially spherical, they are not well designed to reproduce the large scale structures which exhibit clusters, filaments and non spherical voids. This is the reason why Szekeres models, which are devoid of any symmetry, have recently come into play. In this paper, we give the equations and an algorithm to compute the redshift-drift for the most general quasi-spherical Szekeres (QSS) models with no dark energy. We apply it to a QSS model recently proposed by Bolejko and Sussman (BSQSS model) who averaged their model to reproduce the density distribution of the Alexander and collaborators' LTB model which is able to fit a large set of cosmological data without dark energy. They concluded that their model represents a significant improvement over the observed cosmic structure description by spherical LTB models. We show here that this QSS model is ruled out by a negative cosmological redshift, i.e. a blueshift, which is not observed in the Universe. We also compute a positive redshift and the redshift-drift for the Alexander et al.'s model and compare this redshift-drift to that of the $\Lambda$CDM model. We conclude that the process of averaging an unphysical QSS model can lead to obtain a physical model able to reproduce our observed local Universe with no dark energy need and that the redshift-drift can discriminate between this model and the $\Lambda$CDM model. For completeness, we also compute the blueshift-drift of the BSQSS model.

研究动机与目标

• 推导无暗能量的准球对称Szekeres（QSS）模型中红移与红移-漂移的一般方程。
• 将这些方程应用于Bolekjo-Sussman（BSQSS）模型，即一种空间平均的QSS模型，其密度分布与Alexander等人的LTB模型相似。
• 检验平均过程是否能将不合理的特征（如蓝移）转化为物理上可接受的特征。
• 将平均后的BSQSS模型与Alexander等人的LTB模型的红移-漂移特性与ΛCDM模型进行比较。
• 评估尽管信号幅度较小，红移-漂移在区分非均匀模型与ΛCDM模型方面的潜力。

提出的方法

• 利用仅含尘埃的爱因斯坦方程精确解，推导最一般准球对称Szekeres（QSS）模型中红移与红移-漂移的微分方程。
• 开发一种数值算法，沿QSS几何中的类光测地线积分红移与红移-漂移方程。
• 将该算法应用于BSQSS模型，即一种旨在模仿Alexander等人的LTB模型密度分布的空间平均QSS模型。
• 使用一致的数值方法，计算BSQSS模型与原始Alexander等人的LTB模型的红移与红移-漂移。
• 将所得红移-漂移曲线与ΛCDM模型的曲线进行比较，以评估其可区分性。
• 评估未来仪器（如CODEX/EXPRESSO与DECIGO/BBO）对红移-漂移信号的可测量性。

实验结果

研究问题

• RQ1 Bolekjo-Sussman准球对称Szekeres模型（BSQSS）预测宇宙学红移还是蓝移？这与观测是否一致？
• RQ2 空间平均过程能否将一个不合理的QSS模型（具有蓝移）转化为物理上可行的宇宙学模型？
• RQ3 平均后的BSQSS模型的红移-漂移与ΛCDM模型在数量上如何比较？
• RQ4 在高红移（z > 2）处，红移-漂移测量能否区分平均后的QSS模型与ΛCDM模型？
• RQ5 BSQSS模型与Alexander等人的模型中红移-漂移信号的预期幅度是多少？是否可被未来仪器测量？

主要发现

• BSQSS模型预测宇宙学蓝移（负红移），这在宇宙中未被观测到，因此该模型作为物理模型被排除。
• 平均过程将BSQSS模型中不合理的蓝移转化为与观测一致的物理宇宙学红移。
• 尽管信号幅度较小，平均后的BSQSS模型的红移-漂移在原则上可与ΛCDM模型区分开来。
• Alexander等人的LTB模型中红移-漂移信号为正且极小，z ∼ 0.085时十年间的变化量仅为|δz| ∼ 2.10−11。
• BSQSS模型中的红移-漂移信号也极其微弱，当前或近未来仪器（如CODEX/EXPRESSO）无法测量。
• 研究表明，若基于QSS的更复杂、非对称的“瑞士奶酪”模型能达到更高红移（z > 2）并产生可测量信号，则原则上可通过红移-漂移进行检验。