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General relativity and cosmology course
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Module 9
Cosmological Perturbation Theory
1
SVT Decomposition of Metric and Matter Perturbations
Decompose metric and matter perturbations into scalar, vector, and tensor modes (SVT decomposition).
2
Gauge Freedom and Invariant Variables in Perturbation Theory
Explain the concept of gauge freedom in perturbation theory and construct gauge-invariant variables (e.g., Bardeen potentials).
3
Linearized Einstein Equations for Scalar Perturbations
Derive the linearized Einstein equations for scalar perturbations in an expanding background.
4
Quantum Origins of Cosmic Structure
Model quantum fluctuations of the inflaton field during inflation as the origin of primordial perturbations.
5
Primordial Power Spectrum Calculation
Calculate the power spectrum of primordial curvature perturbations generated during inflation.
6
Perturbation Evolution in Radiation- and Matter-Dominated Eras
Analyze the evolution of perturbations after they re-enter the horizon during radiation- and matter-dominated eras.
Transfer Functions and the Matter Power Spectrum
Define the transfer function and its role in shaping the matter power spectrum.
8
Sachs-Wolfe Effect and CMB Anisotropies
Derive the Sachs-Wolfe effect, relating gravitational potential perturbations on the last scattering surface to CMB temperature anisotropies.
Previous module
Quantum Fields in Curved Spacetime
Next module
Advanced Topics in Gravity