GGI Lectures on Large-Scale Structure Perturbation Theory (Effective Field Theory)
Mikhail M. Ivanov
astro-ph.CO, gr-qc, hep-ph, hep-th
Submitted: 2026-07-30
Comments: 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
License: http://creativecommons.org/licenses/by/4.0/
The gist: These notes are an introduction to non-linear perturbation theory for cosmological large-scale structure.
Terminology
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.
Sources
- Cosmological Non-Linearities as an Effective Fluid
- The Effective Field Theory of Cosmological Large Scale Structures
- Generation of Vorticity and Velocity Dispersion by Orbit Crossing
- On the Velocity in the Effective Field Theory of Large Scale Structures
- Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe
- Non-linear Fields in Generalized Cosmologies
- Loop corrections to the power spectrum for massive neutrino cosmologies with full time- and scale-dependence
- Precise Calibration of the One-Loop Bispectrum in the Effective Field Theory of Large Scale Structure
- Perturbation theory of LSS in the $\Lambda$CDM Universe: exact time evolution and the two-loop power spectrum
- Non-linear perturbation theory extension of the Boltzmann code CLASS
- The New Horizon Run Cosmological N-Body Simulations
- Cosmological perturbation theory at three-loop order
- Planck 2018 results. VI. Cosmological parameters
- The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview
- Effective Field Theory of Large Scale Structure and Newtonian Motion Gauges
- On the non-linear scale of cosmological perturbation theory
- Cosmological perturbation theory in 1+1 dimensions
- The 2-loop matter power spectrum and the IR-safe integrand
- The Effective Field Theory of Large Scale Structures at Two Loops
- Symmetries and Consistency Relations in the Large Scale Structure of the Universe
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