PHYS 571 Physical Cosmology 3 credits Prereqs: None (permission of instructor for undergrads) Evaluation: Extensive detailed homework assignments. Term project and presentation. Texts: Dodelson, Modern Cosmology Optional: Kolb and Turner, The Early Universe Unit: Intro/The Smooth Expanding Universe - Historical Perspectives Physics in Cosmology Units/Scales Structures in the Universe (1 lecture) - Expanding Universe Curved Space Newtonian Cosmology Friedmann Equation Fluid and Acceleration Equations (1.5 lectures) Unit: General Relativity, Cosmology, and Relativistic Fluids - Metrics and Geodesics Vectors and 1-Forms Christoffel Symbols for the FRW Metric (1.5 lectures) - Einstein Equations Applied to Smooth FRW Conformal Time Evolution of Energy Momentum Cosmic Inventory: Photons, Baryons, Dark Matter, Neutrinos, Dark Energy (2 lectures) Unit: Thermal History - Boltzmann Equation for 2 <—> 2 Scattering/Annihilation Maxwell-Boltzmann/Fermi-Dirac/Bose-Einstein Distribution Functions Thermal Cross Sections Saha OR Chemical Equilibrium OR LTE OR Nuclear Statistical Equilibrium (1.5 lectures) - BBN: Deuterium Bottleneck Neutron Abundance Helium Fraction (1.5 lectures) - WIMP Dark Matter: Boltzmann Equation for DM Annihilation Freeze Out and Thermal Abundance WIMP Miracle and Weak-Scale Dark Matter (1.5 lecture) - Recombination: Boltzmann Equation for Free Electron Fraction Xe Saha Approximation Freeze Out of Xe (1 lecture) Unit: First Order Collisional Boltzmann Equations in Cosmology - Boltzmann Equation for the Harmonic Oscillator Collisionless Boltzmann Equation for Photons: Zero Order, First Order (1 lecture) - Compton Collision Term and Photon Baryon Coupling Boltzmann Equation for Photons: Fourier Modes, Opacity (1.5 lectures) - Boltzmann Equation for Cold Dark Matter Moments Overdensity and Velocity Perturbation Equations Boltzmann Equation for Baryons (1.5 lectures) Unit: Initial Conditions and Inflation - Perturbation Equations Deep in the Radiation Epoch Adiabatic vs Isocurvature Initial Conditions (1 lecture) - The Horizon Problem Inflation as a Solution to the Horizon Problem Negative Pressure Scalar Field Inflation Slow-Roll Parameters (1.5 lecture) - Quantizing the Harmonic Oscillator Tensor (Gravitational Wave) Perturbations from Inflation Scalar Curvature Perturbations from Inflation Scalar and Tensor Power Spectra The Bardeen Variable Matching Inflationary Perturbations to Radiation Perturbations (1.5 lectures) Unit: Inhomogeneities - Pressure vs. Gravity Transfer Function / Growth Function Split Large Scales: Super-horizon Solution for Gravitational Potentials Horizon Crossing During Matter Domination (1.5 lectures) - Small Scales: Horizon Crossing During Radiation Domination Subhorizion Evolution (Mezaros Equation) The Growth Function Impact of Dark Energy on Growth (2 lectures) Unit: Anisotropies - Photon and Baryon Acoustic Oscillations Toy Model: Forced Harmonic Oscillator Large Scale Anisotropies: Sachs-Wolfe Effect (1.5 lecture) - Tightly-Coupled Photon-Baryon Fluid Sound Horizon WKB Solution (1.5 lecture) - Diffusion Damping and Last Scattering Free Streaming Visibility Function Line-of-Sight Integral for Anisotropies - (1 lecture) Angular Power Spectra and Gaussian Fluctuations Dependence on Cosmological Parameters - (1 lectures) Background: Students assumed to know ODEs, PDEs, Fourier Analysis, Spherical Harmonics. Assumed undergrad statistical mechanics and gravitational dynamics. Necessary nuclear, atomic, and particle physics is developed as needed. Basic computational and numerical analysis is required throughout. Goal: To provide students with a solid background to understand the cosmological physics literature. In particular, the mathematical and theoretical formalism necessary to describe the smooth expanding Universe, cosmic microwave background fluctuations, and linear perturbations of large scale structure.