1 简介

1.1 摘要

星系红移畸变是由于星系本动速度造成的一种重要的宇宙大尺度结构。 结合红移畸变的精确测量和精确模型，能够精确测量宇宙的结构增长率， 从而限制暗能量状态方程和宇宙学尺度上的引力性质。 第四代暗能量巡天项目将实现红移畸变的精确测量， 但是已有红移畸变理论模型的精度尚无法与之匹配。 本文结合宇宙学理论、统计和数值模拟，以理解、改善红移畸变理论模型存在的若干问题。

本文第一章简要介绍宇宙学的背景知识。 第二章详细介绍主要的红移畸变理论模型，以及已有观测对结构增长率\(f\sigma_8\)的限制结果。 在第三章中，作者提供了一种全新方法，第一次在数值模拟中精确测定了暗晕的速度偏袒。 该速度偏袒，如果偏离1，将直接造成宇宙学系统误差。 作者发现在较大尺度\(k\leq 0.1h/\rm{Mpc}\)时，速度偏袒与1的偏离在\(\sim 1\%\)以内，可以被忽略。 随着尺度减小，偏离1逐渐变得显著，将对基于第四代巡天DESI 等的红移畸变宇宙学产生显著影响。 第四章研究了真实空间到红移空间成团性的映射。 该映射决定了红移畸变效应，可以由成对速度的矩母函数(pairwise velocity moment generating function)完全刻画。 作者通过数值模拟测量了矩母函数，比较了矩展开和累积量(Cumulant)展开的精度，发现累积量展开显著优于矩展开。 另一个主要发现是，要精确刻画\(k\sim 0.2h/\rm{Mpc}\)的红移畸变， 需要包含到4阶的累积量展开，这是已有红移畸变模型无法准确描述的。 在第五章中，作者尝试从二维红移空间功率谱出发，运用深度学习方法直接得到本动速度功率谱及其宇宙学信息。 作者建立了快速生成训练样本的方法，生成了大量训练样本，并展示了初步结果。 文章最后为全文总结。

1.2 abstract

Galaxy redshift space distortion (RSD) is a major large scale structure of the universe, induced by peculiar velocity of galaxies. Combining precision measurement and modelling of RSD, we are able to measure the structure growth rate of the universe accurately, and constrain the nature of dark energy and gravity at cosmological scale. Stage IV dark energy projects will be able to measure RSD to high accuracy, beyond that of existing RSD models. This thesis combines the theory, statistics, and numerical simulations of cosmology, in order to understand and overcome several problems in RSD modelling.

The first chapter briefly introduces modern cosmology. Chapter 2 introduces several models of RSD in details, and summarizes existing measurements of the structure growth rate \(f\sigma_8\) with RSD. In chapter 3, I propose a novel method, which has enabled the first accurate measurement of halo velocity bias in simulations. At scales larger than \(k\leq 0.1h/\rm{Mpc}\), the deviation of velocity bias from unity is within \(\sim 1\%\) and can be safely neglected. At smaller scales, the deviation becomes larger, and will become significant for RSD cosmology based on DESI observations. Chapter 4 studies the mapping of clustering from real to redshift space, which totally determines RSD. This mapping can be completely described by the pairwise velocity moment generating function. I measure the generating function using simulations and compare the moment expansion against the cumulant expansion. I find that the cumulant expansion is significantly better. Another major finding is that, to accurately describe RSD to \(k\sim 0.2h/\rm{Mpc}\), cumulants up to 4th order are required. Existing RSD models fail to include them appropriately. In chapter 5 I attempt to directly learn peculiar velocity and the related cosmological information by deep learning, with direct RSD measurement as input. I design methods of fast generation of training set, generate a large training set, and present preliminary results of deep learning. Chapter 6 summarizes the main results.