Ruprecht Karls Universit├Ąt Heidelberg

The Theory of the Cosmic Microwave Background


In this course, we cover the theory of the cosmic microwave background fluctuations. In particular:

  • The expanding universe
  • Stokes parameters, spin harmonics and E and B modes
  • Cosmological perturbations
  • Gauge freedom and gauge transformations
  • The Boltzmann equation for photons
  • The scattering terms of Boltzmann's equation for photons
  • The multipole expansion
  • The line of sight strategy of solving the multipole hierachy
  • The multipole spectrum of temperature and polarization fluctuations
  • Finding initial conditions for the fluctuations
  • The tight coupling limit before recombination
  • Analytic estimates
  • If time permits: secondary anisotropies

Lecture Notes

You can download the lecture notes new from 02-05-2010 (without a chapter on secondary anisotropies yet).

Further Literature

  • The Cosmic Microwave Background, by Ruth Durrer (2008) ISBN-10: 0521847044
  • Principles of Physical Cosmology by P.J.E Peebles (1993) ISBN-10: 0691019339
  • Fluctuations in the Cosmic Microwave Background, Matthias Zaldarriaga's Thesis
  • Gauge Invariant Cosmological Perturbations, J. M. Bardeen (1980), Phys.Rev.D22:1882-1905,1980

Credit Points

Master students may acquire 4 credit points subject to a written exam at the end of the course.

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