Early Universe

 CMB Lensing
 Talks and Notes

Advanced Cosmology (was Early Universe)

This is a graduate (masters) level course covering:
  • Recap of hot big bang, FRW model, distances, Hubble law
  • Geodesics, redshifting, energy conservation and Friedman equations in GR
  • Equilibrium distributions and thermal history
  • Boltzmann equation (unperturbed), freeze out and relics
  • Problems with the hot big bang
  • Inflation with a scalar field
  • Cosmological perturbation theory
  • Quantum generation of perturbations in inflation
  • Power spectrum predictions from inflation
  • Perturbation evolution and growth after reheating
  • Free streaming and Silk damping
  • Matter power spectrum
  • CMB anisotropies
It is expected that you will have done a previous course in General Relativity. Knowledge of Lagrangian mechanics and quantum field theory is also an advantage, but required results will be quickly introduced when required.

For a more introductory course (without General Relativity) see the Cosmology course, which precedes this one (however this is now taught by Robert Smith with somewhat different content). Note that there is significant overlap in the notes to be self-contained as a recap, topics which should be familiar are marked "revision".


Question sheets:

Open Note Exams
Note that in 2011/2012 the course content was different (Q1 content in now mostly covered in Cosmology). From 2013-2016 the rubric was to answer 2 out of 3 questions in 1hr 30 minutes. From 2017 the time allowed in 2hr. Some of these questions you will have seen before in this year's question sheets.

Books and other notes

There isn't a book that really covers the content of the course at a similar level, but some references may be useful for filling in details not covered by the course, different approaches and further reading. There are also some excellent notes by Anthony Challinor, which give full derivations of many things covered in the latter parts of the course, though going significantly beyond it in places. For the most part the notation is consistent. You can also find full derivations in Weinberg's Cosmology. Notes by Daniel Baumann are excellent and may also be useful and more similar in content.

  • Lecture Notes in Cosmology by Oliver F. Piattella
    Free download from arXiv, many parts of the course covered.
  • Introduction to Cosmology by Barbara Ryden
    Updated 2016: Slightly lower level, but covers many similar topics plus reminder of the basics
  • Modern Cosmology by Scott Dodelson
    Updated 2003: A good reference, though differences in depth of coverage of different topics
  • The Primordial Density Perturbation by David Lyth and Andrew Liddle
    Updated 2009: Good reference for inflation and perturbations, but going well beyond the level of the course
  • Physical Foundations of Cosmology by Viatcheslav Mukhanov
    Mostly much more advanced, but Chapter 3 has useful material on thermal history
  • Cosmological Physics by John Peacock
    From 1998, so getting a bit old, but plenty of useful material
  • Cosmology by Steven Weinberg
    Does everything from first principles, going significantly further in places. Maybe a useful reference, but probably not the easiest place to start.
  • Primordial Cosmology by Patrick Peter
    2013: I don't have it, but includes some similar material and goes further into more advanced topics
  • Cosmic Microwave Background by Ruth Durrer
    2008: Much more mathematical and advanced, but a reference for more detail on sections about the CMB
  • Spacetime and Geometry by Sean Carroll
    A nice GR text book, may be a useful reference for some GR-related topics
  • An Introduction to Modern Cosmology by Andrew Liddle
    Updated 2015: Lower level, but may be useful for reminder of basics
  • Introduction to Cosmology by Matts Roos
    Updated 2015: I've not seen it
Toy problem worksheet on power spectra and transfer functions


There's also a MatLab script for generating 2D Gaussian random fields with a given spectrum (n_s).

Extra off-syllabus material

Some of the derivations are rather long, and not included in the notes or lectures, e.g. the perturbed Einstein equations and the second order action for calculation the fluctuations in inflation. The course only aims to cover the starting point and results, and important physics, rather than lots of tedious calculation of Christoffel symbols. If you are interested here are some Maple worksheets using GRTensor for calculating some of these results. Sorry these are not well documented, and in some places well beyond the level of the course