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| The Standard Model and Beyond | |
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| The Expanding Universe | |
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| The Hubble Diagram | |
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| Big Bang Nucleosynthesis | |
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| The Cosmic Microwave Background | |
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| Beyond the Standard Model | |
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| Summary | |
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| Exercises | |
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| The Smooth, Expanding Universe | |
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| General Relativity | |
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| The Metric | |
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| The Geodesic Equation | |
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| Einstein Equations | |
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| Distances | |
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| Evolution of Energy | |
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| Cosmic Inventory | |
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| Photons | |
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| Baryons | |
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| Matter | |
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| Neutrinos | |
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| Dark Energy | |
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| Epoch of Matter-Radiation Equality | |
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| Summary | |
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| Exercises | |
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| Beyond Equilibrium | |
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| Boltzmann Equation for Annihilation | |
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| Big Bang Nucleosynthesis | |
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| Neutron Abundance | |
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| Light Element Abundances | |
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| Recombination | |
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| Dark Matter | |
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| Summary | |
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| Exercises | |
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| The Boltzmann Equations | |
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| The Boltzmann Equation for the Harmonic Oscillator | |
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| The Collisionless Boltzmann Equation for Photons | |
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| Zero-Order Equation | |
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| First-Order Equation | |
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| Collision Terms: Compton Scattering | |
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| The Boltzmann Equation for Photons | |
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| The Boltzmann Equation for Cold Dark Matter | |
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| The Boltzmann Equation for Baryons | |
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| Summary | |
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| Exercises | |
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| Einstein Equations | |
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| The Perturbed Ricci Tensor and Scalar | |
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| Christoffel Symbols | |
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| Ricci Tensor | |
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| Two Components of the Einstein Equations | |
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| Tensor Perturbations | |
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| Christoffel Symbols for Tensor Perturbations | |
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| Ricci Tensor for Tensor Perturbations | |
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| Einstein Equations for Tensor Perturbations | |
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| The Decomposition Theorem | |
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| From Gauge to Gauge | |
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| Summary | |
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| Exercises | |
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| Initial Conditions | |
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| The Einstein-Boltzmann Equations at Early Times | |
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| The Horizon | |
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| Inflation | |
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| A Solution to the Horizon Problem | |
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| Negative Pressure | |
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| Implementation with a Scalar Field | |
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| Gravity Wave Production | |
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| Quantizing the Harmonic Oscillator | |
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| Tensor Perturbations | |
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| Scalar Perturbations | |
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| Scalar Field Perturbations around a Smooth Background | |
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| Super-Horizon Perturbations | |
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| Spatially Flat Slicing | |
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| Summary and Spectral Indices | |
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| Exercises | |
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| Inhomogeneities | |
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| Prelude | |
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| Three Stages of Evolution | |
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| Method | |
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| Large Scales | |
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| Super-horizon Solution | |
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| Through Horizon Crossing | |
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| Small Scales | |
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| Horizon Crossing | |
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| Sub-horizon Evolution | |
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| Numerical Results and Fits | |
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| Growth Function | |
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| Beyond Cold Dark Matter | |
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| Baryons | |
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| Massive Neutrinos | |
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| Dark Energy | |
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| Exercises | |
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| Anisotropies | |
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| Overview | |
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| Large-Scale Anisotropies | |
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| Acoustic Oscillations | |
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| Tightly Coupled Limit of the Boltzmann Equations | |
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| Tightly Coupled Solutions | |
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| Diffusion Damping | |
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| Inhomogeneities to Anisotropies | |
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| Free Streaming | |
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| The C[subscript l]'s | |
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| The Anisotropy Spectrum Today | |
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| Sachs-Wolfe Effect | |
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| Small Scales | |
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| Cosmological Parameters | |
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| Curvature | |
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| Degenerate Parameters | |
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| Distinct Imprints | |
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| Exercises | |
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| Probes of Inhomogeneities | |
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| Angular Correlations | |
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| Peculiar Velocities | |
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| Direct Measurements of Peculiar Velocities | |
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| Redshift Space Distortions | |
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| Galaxy Clusters | |
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| Exercises | |
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| Weak Lensing and Polarization | |
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| Gravitational Distortion of Images | |
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| Geodesics and Shear | |
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| Ellipticity as an Estimator of Shear | |
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| Weak Lensing Power Spectrum | |
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| Polarization: The Quadrupole and the Q/U Decomposition | |
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| Polarization from a Single Plane Wave | |
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| Boltzmann Solution | |
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| Polarization Power Spectra | |
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| Detecting Gravity Waves | |
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| Exercises | |
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| Analysis | |
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| The Likelihood Function | |
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| Simple Example | |
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| CMB Likelihood | |
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| Galaxy Surveys | |
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| Signal Covariance Matrix | |
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| CMB Window Functions | |
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| Examples of CMB Window Functions | |
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| Window Functions for Galaxy Surveys | |
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| Summary | |
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| Estimating the Likelihood Function | |
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| Karhunen-Loeve Techniques | |
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| Optimal Quadratic Estimator | |
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| The Fisher Matrix: Limits and Applications | |
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| CMB | |
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| Galaxy Surveys | |
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| Forecasting | |
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| Mapmaking and Inversion | |
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| Systematics | |
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| Foregrounds | |
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| Mode Subtraction | |
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| Exercises | |
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| Solutions to Selected Problems | |
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| Numbers | |
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| Physical Constants | |
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| Cosmological Constants | |
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| Special Functions | |
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| Legendre Polynomials | |
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| Spherical Harmonics | |
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| Spherical Bessel Functions | |
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| Fourier Transforms | |
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| Miscellaneous | |