Graduate Course: QFT for Cosmology

Quantum Field Theory for Cosmology

AMATH872 / PHYS785

Winter 2010

Instructor: A. Kempf,  (MC6071, ext. 35462)
Prerequisite: AMATH 673, PHYS702 or consent of instructor. Some knowledge of General Relativity.
Time:   Tuesdays 4-5:20pm + Thursdays 5-6:20pm
Venue: Perimeter Institute's Bob room 
Video-linked to:
     *  Univ. of Waterloo, Room MC6091
     *  Univ. of Guelph, Rozanski Room 106
     *  possibly other venues upon request
         (at via H323)
Office hours: by arrangement



Final exam date:  Monday, April 12th, time: 2-3:30pm, PI, Bob room.

Essay deadline: Sunday, April 18, 11:59pm



This course begins with a thorough introduction to quantum field theory. Unlike the usual quantum field theory courses which aim at applications to particle physics, this course then focuses on those quantum field theoretic techniques that are important in the presence of gravity. In particular, this course introduces the properties of quantum fluctuations of fields and how they are affected by curvature and by gravitational horizons. We will cover the highly successful inflationary explanation of the fluctuation spectrum of the cosmic microwave background - and therefore the modern understanding of the quantum origin of all inhomogeneities in the universe (see these amazing visualizations from the data of the Sloan Digital Sky Survey. They display the inhomogeneous distribution of galaxies several billion light years into the universe: Sloan Digital Sky Survey).


  • From first to second quantization.
  • Introduction to scalar quantum field theory.
  • The Unruh effect.
  • Canonical quantization in curved space-times.
  • Path integral quantization of fields
  • Quantum fluctuations of scalar fields and of the metric.
  • Applications: Inflationary cosmology and the origin of structure.
  • (Time permitting:) Effective action and gravitational backreaction

Lecture notes:  

Detailed lecture notes, written on a Tablet PC, will be made freely available here, usually a few days before each lecture, here:

Lecture notes of W10:    1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23

Note: If you have read the lecture notes or viewed the recordings without having being enrolled in the course, would you mind sending me an email please? I'd just like to know. Thanks!

The video recordings of the lectures are posted here.

You may also be interested in viewing the colloquium that I gave at Perimeter Institute on Sep.16, 2009:
"Spacetime can be simultaneously continuous and discrete, in the same way that information can".
For the recording, see here.

Additional Literature:

  • We will often follow this text:
    V. Mukhanov, Sergei Winitzki, Introduction to Quantum Effects in Gravity, Cambridge University Press, June 2007

Note that this text includes problems with solutions.

  • Other recommended texts are:
    • N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space, CUP, 1984.
    • S. A. Fulling, Aspects of Quantum Field Theory in Curve Space-Time, CUP, 1989.
    • A. R. Liddle, D. H. Lyth, Cosmological Inflation and Large-Scale Structure, CUP, 2000.
    • T. Jacobson, Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect, freely available at
    • L.H. Ford, Quantum Field Theory in Curved Spacetime, freely available at


An essay should be a review of existing literature on a given topic. The sources can be textbooks or review articles or original articles or some of each. Most articles are now available online and for example "Google Scholar" can get you there quickly. Most electronic journals require subscription, which our library usually has. For the license to be recognized you will need to either browse from a university computer (the domain is what counts) or you log into the UW library from home and go to an electronic journal through our library's electronic journal search engine. 

Essay topics:

  • Rationale for and models of inflationary cosmology (with or without a focus, for examle a focus on multi-field inflation)
    Literature suggestions: The text book by Liddle and Lyth (see above), An exposition of Inflationary Cosmology, by G.S.Watson.
  • Planck scale effects in inflationary cosmology
    Literature suggestions:   Brandenberger et al.Kempf et al., Greene et al, see also Brian Greene's talk online.
  • Calculation and simulation of quantum fluctuations and their amplification in inflationary cosmology.
    Literature: our lecture notes.
  • Sonic analog of black holes and Hawking radiation
    Literature suggestions: Unruh1, Unruh2 (link works on campus machines), Unruh3, Brout et al
  • Perhaps other topics: make a suggestion.

Consider also other sources, e.g., other texts and this electronic archive (*). See also this talk online.

What is expected in an essay:

Show that you have understood and critically reflected upon the material by making it your own. You make it your own by coming up with an original way for presenting the material that you are bringing together. Try to give it your own angle or spin. Wherever possible, try to put things into the larger context. Sometimes (hopefully very rarely) it is necessary to stick quite closely to a source, e.g., when a calculation is to be presented and the source just does it in a way that is hard to improve. In this case, you can make it your own by filling in steps in trhe calculation that the author omitted (and point out that you do so). That obviously proves that you understood that calculation. No original research is expected but try to become sufficiently familiar with the topic that you can make educated speculations about what interesting things could be done in this area. Feel free to mention what comes to mind. Show creativity. In research, just asking the right questions is often the key to breakthroughs.

Essay format:

  • Length: 15-20 pages, pdf format
  • Format: title+abstract page / introduction / main parts / summary (or conclusions) / bibliography
  • It is very important that you refer to your sources explicitly, i.e. the bibliography is very important. List items in the sequence in which you are referring to them in the text.

Relationship to other courses:

This course is one in a group of four related graduate courses whose curricula have been coordinated so as to optimally complement another:

  • AMATH875/PHYS786, General Relativity for Cosmology, taught F09, F11 etc., see GR for Cosmology.
  • PHYS784/AMATH874,  Advanced Techniques in General Relativity and Applications to Black Holes, taught W08, W10 etc.
  • AMATH872/PHYS785, Introduction to Quantum Field Theory for Cosmology, (this course) taught W08, W10 etc.
  • PHYS703,AMATH873, Quantum Field Theory (for high energy physics), taught W09, W11 etc.

These courses can be taken in arbitrary sequence and no course is a pre- or anti- requisite for another.


The final will count 40%, the essay 60%.

Last Modified:  12 January 2010