This course will have a heavy emphasis on the theory of cosmic microwave background anisotropies.

Its goal is to provide the student with a sufficient knowledge of their calculation in the standard cosmological model that they will be able to make custom modifications to the calculations with the help of CMBfast.
 

I will be using Scott Dodelson's book as a reference source. Copies can be printed from this pdf and additional ones will be made available to registered students.

Requirements for this course are the 300 level cosmology series in the Astronomy and Astrophysics department (or suitable graduate level introduction to cosmology).

There will be approximately 1 problem per lecture as homework with perhaps a longer final problem set or optional oral presentation (to be decided).

M: 1:30-3:00
W: 1:30-3:00

I will be away Jan 8 and Jan 10.  I will try to reschedule these lectures to accomodate everyone's schedules.

The syllabus is divided into pairs of lectures labelled weeks.  The actual correspondence to given days will vary and topics in the 9th and 10th weeks may fall off the edge of the course.
 

Week 1

1.1  Overview

• Overview/Goals of the Course
• A General Intro to CMB Anisotropies (laptop style presentation)

1.2  FRW Cosmology

• FRW metric
• Comoving/conformal coordinates
• Friedman equations
• Horizon
• Distance measures

Week 2

2.1  Thermal History

• Nucleosynthesis and the Prediction of the CMB
• Thermalization and the establishment of a blackbody
• Matter Radiation Equality
• Recombination
• Compton drag and Thermal Decoupling
• Reionization

2.2  Linear Perturbation Theory: General Aspects

• The perturbed Einstein equation
• Scalar, vector, tensor decomposition.
• Covariant scalar einstein equations
• Scalar gauge freedom

Week 3

3.1  Linear Perturbation Theory: Specifics

• Useful scalar gauges and their interpretation
• Tensor Einstein equations

3.2  Initial Conditions & Inflation

• Problems of the "standard" model
• Scalar field equation
• Slow roll and its parameters
• Scalar and tensor amplitudes
• Gravity wave - tilt and consistency relation.

Week 4

4.1  Acoustic Oscillations: Kinematic Effects

• Sachs-Wolfe effect
• Tight coupling approximation
• Temperature oscillations
• Velocity oscillations
• Baryon effects

4.2  Acoustic Oscillations: Dynamical Effects

• Driving effects: Matter/Radiation, defects...
• Damping effects: Radiative viscosity and heat conduction

Week 5

5.1  The Boltzmann Equation: Normal Modes

• Mode Decomposition
• Spherical Harmonics
• Spin Spherical Harmonics
• Free streaming and the Liouville equation

5.2  The Boltzmann Equation: Scattering

• Thomson differential cross section
• Chandra's scattering matrix
• The hierarchy equations

Week 6

6.1  The Boltzmann Equation: Solutions

• Coupling of angular momenta
• Scalar projection
• Tensor projection
• Mechanics of CMBFast

6.2  Polarization

• Quadrupole sources
• E and B revisited
• Scalar / Acoustic contributions
• Reionization
• Tensors and B

Week 7

7.1  Parameter Estimation

• Fisher matrix
• Forecasts
• Band Powers
• Data analysis issues

7.2  Relation to Large Scale Structure

• COBE Normalization
• Growth Rates
• Transfer function
• Non-linear regime

Week 8

8.1  Secondary Anisotropies: General Structure

• Gravitational Effects
• Scattering Effects
• Slowly varying sources
• Weak Coupling and Limber Approximation

8.2  Secondary Gravitational Effects

• Gravitational Redshifts: ISW and RS Effects
• Gravitational Lensing

Week 9

9.1  Secondary Scattering Effects

• Optical Depth Suppression
• Doppler Effect and Cancellation
• Modulated Doppler Effects, Vishniac, Kinetic SZ, Patchy Reionization

9.2  Thermal SZ Effect

• The Kompaneets equation
• SZ effect
• Clusters
• Effect on Power Spectrum
• Foreground separation

Week 10

10.1  Non-Gaussianity

• The Bispectrum
• The Trispectrum
• Gravitational Lensing Example

10.2  Review and Data Update