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.