AI 中文总结
本讲义面向无相关背景的学生，系统介绍宇宙学大规模结构非线性微扰理论，涵盖有效场论、标准微扰理论缺陷、星系偏差等内容，最终引入拉格朗日微扰理论。
AI 中文摘要
本讲义是宇宙学大规模结构非线性微扰理论的入门内容，面向本科生和低年级研究生，无需宇宙学或量子场论背景，所有必要概念均从零推导。讲座旨在解释建模真实空间和红移空间中观测到的星系成团所需的全部关键要素。在对有效场论（EFT）理念进行简要教学式介绍后，我们利用对称性原理在牛顿宇宙学框架下构建大规模结构 EFT。我们详细讨论了标准微扰理论的缺陷、重子声学振荡的非线性演化及其与等效原理的关系、圈图的抵消项和重整化，以及随机效应。随后我们构建星系偏差和红移空间畸变的 EFT，还强调了与当前及未来星系巡天相关的红移空间随机性的重要事实，最后介绍拉格朗日微扰理论。
英文摘要
These notes are an introduction to non-linear perturbation theory for cosmological large-scale structure. They are aimed at undergraduate and beginning graduate students and do not require any cosmology or quantum field theory background. All necessary concepts are developed from scratch. The lectures are intended to explain all key ingredients needed to model the observed clustering of galaxies in real and redshift spaces. After a brief pedagogical introduction to the ideas of effective field theory (EFT), we develop large-scale structure EFT in the context of Newtonian cosmology using symmetry principles. We discuss in detail the shortcomings of Standard Perturbation Theory, the non-linear evolution of baryon acoustic oscillations and its relation to the equivalence principle, counterterms and renormalization of the loop diagrams, and stochastic effects. Then we develop EFT for galaxy bias and redshift space distortions. We also highlight some important facts about redshift-space stochasticity, relevant for ongoing and future galaxy surveys. Finally, we introduce Lagrangian Perturbation Theory.
Comments87 pages, 19 figures, an extended version of lectures delivered at the "New Physics from Galaxy Clustering'' school at the Galileo Galilei Institute, Florence, in August 2025
