XIIth School of Cosmology
September 15 - 20, 2014IESC, Cargèse
their impact in the study of galaxies and

Averaging Inhomogeneous Cosmologies

Université Lyon 1 (


  1. Averaging in Newtonian Cosmology
  2. Averaging in Relativistic Cosmology


In this course we address the averaging problem both in Newtonian Cosmology and in Relativistic Cosmology. We introduce in each theory the basic equations and propose to spatially average the scalar parts of the general equations without further restricting the problem. The result are effective cosmological equations that are discussed with respect to a number of aspects:
  1. Non-commutativity of averaging and time-evolution
  2. Backreaction terms
  3. Integral properties of Newtonian models and their relation to morphological measures
  4. Newton’s iron sphere theorem
  5. The architecture of numerical simulations in cosmology
  6. Coupling of matter inhomogeneities to intrinsic curvature in relativistic models
  7. Relations to information theoretical measures
  8. Relation to scalar field theories
  9. Global gravitational instability and far-from-equilibrium state equations
  10. Cosmological principles and the global topology of the Universe
  11. Examples of averaged inhomogeneous cosmologies and comparison with the standard model of cosmology
  12. Dark Energy and Dark Matter problems


  • Articles
    • "Dark Energy from Structure: A Status Report"
      Thomas Buchert. Gen. Rel. Grav. 40: 467-527, 2008. e–Print: arXiv:0707.2153
    • "Toward physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects"
      Thomas Buchert. Class. Quant. Grav. 28: 164007, 2011. e–Print: arXiv:1103.2016
    • "Backreaction in late–time cosmology"
      Thomas Buchert, Syksy Rasanen. Ann. Rev. Nucl. & Part. Phys. 62: 57, 2012. e–Print: arXiv:1112.5335
    • "Inhomogeneity effects in cosmology"
      George F R Ellis. Class. Quant. Grav. 28, 164001 (2011). e–print: arXiv:1103.2335
    • "Does the growth of structure affect our dynamical models of the Universe? The averaging, backreaction, and fitting problems in cosmology"
      Chris Clarkson, George Ellis, Julien Larena, Obinna Umeh. Rep. Prog. Phys. 74, 112901 (2011). e–print: arXiv:1109.2314
  • Lecture Notes can be uploaded here