Introductory Overview of Eulerian & Lagrangian Perturbation Theories

1 THE FLUID EQUATIONS 2 1.1 Microscopic Description 2 1.2 Macroscopic Description 3 1.3 Velocity Moments and the Fluid Limit 3 2 EULERIAN PERTURBATIVE SOLUTIONS 4 2.1 Linear Density Field 4 2.2 Linear Peculiar Velocity Field 6 2.3 Non-Linear Corrections 7 3 SOME BASIC APPLICATIONS 8 3.1 The PDF as a Measure of Large Scale Structures 8 3.2 Moments of the PDF 9 3.3 Edgeworth Expansion of the PDF 12 3.4 Validity of Perturbation Theory 13 4 FURTHER DEVELOPMENTS 15 4.1 Higher Order Moments 15 4.2 Higher Order Corrections to the Moments 15 4.3 General Initial Conditions 16 4.4 Biasing and comparisons to data 16 5 ZELDOVICH APPROXIMATION 18 5.1 Derivation from Eulerian Theory 18 5.2 Galactic Spin Origin 19 5.3 Density Contrast & Pancakes 19 6 LAGRANGIAN PERTURBATION THEORY 20 6.1 Perturbative equations 21 6.2 Low order Solutions 22 7 APPLICATIONS 24 7.1 Moments in the Lagrangian approach 24 7.2 Redshift Space Skewness 25 7.3 Approach of the Non-Linear Regime 26 8 CONCLUSIONS 27