Table of contents

Back to the main page 1. Lecture notes 2. Literature

Lecture notes

The theory needed in this course is covered in Dodelson and Baumann, but we also provide a comprehensive set of lecture notes given below including videos where we go through the lectures. The topics covered are grouped by what you need to know to complete each milestone in the numerical project.

Overview of the course

[Milestone I] A Crash course in General Relativity - The Rise of the Einstein tensor:

[Milestone I] Background cosmology - Revenge of the Cosmological Constant:

[Milestone II] Thermodynamics/statistical mechanics and the thermal history of our Universe - The Photons Strikes Back:

[Milestone III] Cosmological perturbation theory - Return of the Einstein Tensor:

[Milestone III] Initial conditions and the theory of inflation - A New Hope for Isotropy:

[Milestone IV] From perturbations to statistical observables and evolution of the perturbations - The Power-Spectrum Awakens:

[Milestone V] Non-linear structure-formation (not in the curriculum):

[Appendix] Units in cosmology:

[Appendix] Numerical methods:

[Appendix] Some math needed in this course (will be introduced as we go along):



For a textbook that covers the theoretical background needed for this course see Dodelson "Modern Cosmology" (2003). A brand new second edition of this book, written by Scott Dodelson and Fabian Schmidt, was released in 2020 and contains many modern developments.

There are some very good lecture notes online for example Daniel Baumann's notes from Cambridge (which is basically a book) is very good. The presentation here is a bit more theoretical than Dodelson so it depends on what you like best. I strongly reccomend both this and Dodelson's book.

For cosmology generally, Weinberg is a great reference. For most people it will not be a good book to learn cosmology from, since it goes into tedious detail in all the arguments, but if you want a rigorous treatment or want to understand some detail that is skipped or handwaved away in a usual textbook, then this is the book to look at: S. Weinberg, "Cosmology", Oxford University Press (2008).

For learning more about General Relativity I highly recommend Sean Carrol's book, thorough and clear with a good section on cosmology: S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity", Addison Wesley (2004).

You can find a PDF with the lecture notes Sean Carroll's book is built on here. For a more compressed introduction to General Relativity I reccommend A No-Nonsense Introduction to General Relativity by Sean Carroll. For a summary of what you need to know about General Relativity in this course see this note by Haavard Ihle or this note by Øystein Elgarøy. There is also some material given in the leture notes below.

Here are some lecture notes from PhD winther/summer schools that are very nice. They are very dense, but contains a good summary of all the material we are going to go through in this course. More relevant for PhD students and to use as reference materials. Lecture Notes on CMB Theory: From Nucleosynthesis to Recombination by Wayne Hu. Covariant Linear Perturbation Formalism by Wayne Hu. Physics of the Cosmic Microwave Background Radiation by David Wands, Oliver F. Piattella and Luciano Casarini. Wandering in the Background: A CMB Explorer by Wayne Hu (PhD Thesis).

Here are some very good lecture notes that covers most of the theory we are going through in this course written in Norwegian:

Research papers

Petter Callin has written a great low-level review "How to compute the CMB spectrum" that has all the equations, some programming techniques and some plots that you can use to compare your results to. This is suitable for everybody and we will use the same notation as they do in this paper. You should read this paper for the numerical project.

Another great paper is Chung-Pei Ma and Edmund Bertschinger "Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges". It's written at a much higher level than the paper above so if you are new to cosmology stick with the one above. The paper presents a systematic treatment of the linear theory of scalar gravitational perturbations in both the synchronous gauge and the conformal Newtonian gauge. It gives a complete discussion of all particle species that are relevant to any flat cold dark matter model: cold dark matter, baryons, photons, massless neutrinos and massive neutrinos.

A more modern version of what the paper above does and also a much more complete description of how to solve for the CMB including all possible geometries for both scalar, vector and tensor perturbations is A Complete Treatment of CMB Anisotropies in a FRW Universe by Wayne Hu, Uros Seljak, Martin White and Matias Zaldarriaga.

A great classical paper on cosmological perturbation theory is Gauge-independent cosmological perturbations by James Bardeen.

Some other good papers for including additional physical effects (that we don't cover in this course):

Some papers from experiments that have measured the CMB and the cosmological parameters constraints they obtained (see also List of cosmic microwave background experiments for a complete list of 50+ experiments performed to date):

Various slides used in lectures