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Course Details - Cosmology III - Cosmological Perturbation Theory
Instructor:
Simerdeep Singh
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Sample of Cosmology III - Cosmological Perturbation Theory
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1 Category1
1.1 Group1
1.1.1 Course Information
1.1.1.1 Teacher
1.1.1.2 YouTube Playlist
1.1.1.3 Prerequisites
1.1.1.4 Learning Goals
1.1.1.5 Truths
1.1.1.6 Feedback
1.1.1.7 Financial Support
1.1.1.8 Best Wishes
1.1.1.9 Care for Children
1.1.2 The Perturbed Universe
1.1.2.1 Abstract
1.1.2.2 A Cosmological Field
1.1.2.3 Remarks
1.1.2.4 Homogeneous and Isotropic Universe
1.1.2.5 The Background 3-Space Metric
1.1.2.6 The Minkowski Metric
1.1.2.7 The Background Metric
1.1.2.8 Inhomogeneous and Anisotropic Universe
1.1.2.9 The First Equation
1.1.2.10 The Spatial Average
1.1.2.11 More than One Coordinate Systems
1.1.2.12 Some Optional Fun
1.1.2.13 A Perturbed Gauge
1.1.2.14 Two Perturbed Gauges
1.1.2.15 The Transformation Vector
1.1.2.16 One Set of Coordinates
1.1.2.17 The First Equation in Gauge 1 and Gauge 2
1.1.2.18 The First Equation for a Scalar Field
1.1.2.19 The First Equation for a Vector Field
1.1.2.20 The First Equation for a Tensor Field
1.1.3 Some Helpful Equations
1.1.3.1 Abstract
1.1.3.2 The First Theorem
1.1.3.3 The Background Vectors
1.1.3.4 The Background Tensors
1.1.3.5 A Useful Approximation
1.1.3.6 Two More Approximantions
1.1.3.7 Another Approximation
1.1.3.8 Relating the Coordinates of P1 and P2
1.1.3.9 The Transformation Matrices
1.1.3.10 Linear Perturbation Theory
1.1.4 Transformations at One Point
1.1.4.1 Abstract
1.1.4.2 From General Relativity
1.1.4.3 Vector Transformation
1.1.4.4 Tensor Transformation
1.1.5 Review 1
1.1.5.1 Review 1
1.1.6 Transformations at One Set of Coordinates
1.1.6.1 Abstract
1.1.6.2 A Useful Relationship
1.1.6.3 Scalar Field
1.1.6.4 Vector Field
1.1.6.5 Tensor (0,2) Field
1.1.6.6 Tensor (1,1) Field
1.1.6.7 Tensor (2,0) Field
1.1.6.8 Notation Simplification
1.1.7 Review 2
1.1.7.1 Review 2
1.1.8 Introduction to Linear Decomposition
1.1.8.1 Abstract
1.1.8.2 An Example from High School Physics
1.1.8.3 An Example from Undergraduate Physics
1.1.9 Linear Decomposition of Scalar Perturbations
1.1.9.1 Abstract
1.1.9.2 Fourier Decomposition
1.1.9.3 Useful Fourier Expressions
1.1.9.4 Dropping the Subscript k in the Fourier Space
1.1.10 Linear Decomposition of Vector Perturbations
1.1.10.1 Abstract
1.1.10.2 Helmholtz Decomposition-1 (Introduction)
1.1.10.3 Helmholtz Decomposition-2 (Longitudinal Pa...
1.1.10.4 Helmholtz Decomposition -3 (Wave Vector al...
1.1.11 Linear Decomposition of Tensor(0,2) Perturbations
1.1.11.1 Abstract
1.1.11.2 3X3 Trace and Traceless Parts
1.1.11.3 SVT Decomposition
1.1.11.4 Symmetric and Traceless Scalar Component
1.1.11.5 Symmetric and Traceless Vector Component
1.1.11.6 Symmetric and Traceless Tensor Component
1.1.11.7 Fourier Decomposition of 00 (Scalar)
1.1.11.8 Fourier Decomposition of 0i and i0 (Scalar...
1.1.11.9 Fourier Decomposition ij (Scalar, Vector a...
1.1.11.10 The Wave Vector along the z-axis
1.1.11.11 4 x 4 SVT Matrices
1.1.12 Linear Decompositions and Gauge Transformations
1.1.12.1 Introduction
1.1.12.2 00 Component
1.1.12.3 0i and i0 Components
1.1.12.4 ij Components
1.1.12.5 Decomposition Strategy 1
1.1.12.6 Decomposition Strategy 2
1.1.12.7 Gauge Freedom
1.1.12.8 Gauge Independent Scalar Potentials
1.1.13 Review 3
1.1.14 Metric Tensor
1.1.14.1 Non-Expanding Background Universe
1.1.14.2 Expanding Background Universe
1.1.14.3 Exercise
1.1.14.4 Perturbed Non-Expanding Universe
1.1.14.5 Perturbed Expanding Universe
1.1.14.6 Decomposition of B_i
1.1.14.7 Decomposition of h_ij
1.1.14.8 SVT Decomposition
1.1.14.9 Gauge Transformation of Scalars
1.1.14.10 Exercise
1.1.14.11 Inverse of Perturbed Metric
1.1.14.12 Exercise
1.1.14.13 Exercise
1.1.14.14 Gauge Independent Scalar Potentials
1.1.14.15 Exercise
1.1.15 Connection Coefficients
1.1.15.1 Six Components
1.1.16 Fluid Velocity
1.1.16.1 Proper Time
1.1.16.2 Three-Velocity
1.1.16.3 Four-Velocity
1.1.16.4 Exercise
1.1.16.5 Background Universe
1.1.16.6 Exercise
1.1.16.7 Perturbed Universe
1.1.16.8 Exercise
1.1.17 Threads, Slices and Worldlines
1.1.17.1 Threads and Slices
1.1.17.2 Orthogonal Worldlines
1.1.17.3 Shift and Lapse
1.1.18 Conformal Newtonian Gauge
1.1.19 Perturbed Curvature
1.1.20 Perturbed Energy-Momentum Tensor
1.1.21 Einstein Equations
1.1.22 Review 4
1.1.23 xxxThe Background Universe
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