GGI Lectures on Large-Scale Structure Perturbation Theory (Effective Field Theory)
arXiv:2607.28314
These lecture notes introduce non-linear perturbation theory and effective field theory methods for modeling the large-scale distribution of galaxies, targeting undergraduate and early graduate students.
Abstract
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.
87 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