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arXiv 2005.02035astro-ph.CO
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宇宙学推论问题中的信息熵

Information entropy in cosmological inference problems

Ana Marta Pinho, Robert Reischke, Marie Teich, Björn Malte Schäfer

摘要:

本文的主题是量化的信息内容的宇宙学探针的大尺度结构,特别是温度和偏振各向异性的宇宙微波背景,CMB透镜,弱宇宙剪切和星系集群,在信息论措施,如信息熵。我们的目标是建立高斯似然的关系,统计不确定性和信息熵的传统措施之间。此外,我们将这些研究扩展到(贝叶斯)证据的计算和测量的能力,以区分竞争模型。我们详细研究了宇宙学数据如何通过减少统计误差和打破简并来降低信息熵。此外,我们还研究了数据集之间的紧张关系如何增加信息熵,并在三个例子中量化了这种影响:CMB和弱透镜之间的$Ω_m$和$σ_8$中的差异,当尝试状态参数的暗能量方程时,弱透镜数据中固有对准的作用,以及著名的$H_0$ -哈勃基石计划中造父变星之间的张力和普朗克观测到的宇宙微波背景。

英文摘要:

The subject of this paper is a quantification of the information content of cosmological probes of the large-scale structures, specifically of temperature and polarisation anisotropies in the cosmic microwave background, CMB-lensing, weak cosmic shear and galaxy clustering, in terms of Information theory measures like information entropies. We aim to establish relationships for Gaussian likelihoods, between conventional measures of statistical uncertainties and information entropies. Furthermore, we extend these studies to the computation of (Bayesian) evidences and the power of measurement to distinguish between competing models. We investigate in detail how cosmological data decreases information entropy by reducing statistical errors and by breaking degeneracies. In addition, we work out how tensions between data sets increase information entropy and quantify this effect in three examples: the discrepancy in $Ω_m$ and $σ_8$ between the CMB and weak lensing, the role of intrinsic alignments in weak lensing data when attempting the dark energy equation of state parameters, and the famous $H_0$-tension between Cepheids in the Hubble keystone project and the cosmic microwave background as observed by Planck.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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