Chapters
 Averaging in Newtonian Cosmology
 Averaging in Relativistic Cosmology
Abstract
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:
 Noncommutativity of averaging and timeevolution
 Backreaction
terms
 Integral properties of Newtonian models and their relation to morphological measures
 Newton’s iron sphere
theorem
 The architecture of numerical simulations in cosmology
 Coupling of matter inhomogeneities to intrinsic curvature in
relativistic models
 Relations to information theoretical
measures
 Relation to scalar field theories
 Global
gravitational instability and farfromequilibrium state equations
 Cosmological principles and the global topology of the Universe
 Examples of averaged inhomogeneous cosmologies and comparison with the
standard model of cosmology
 Dark Energy and Dark Matter problems

Bibliography
 Articles
 "Dark Energy from
Structure: A Status Report"
Thomas
Buchert. Gen.
Rel. Grav. 40: 467527, 2008. e–Print: arXiv:0707.2153
 "Toward physical
cosmology: focus on inhomogeneous geometry and its nonperturbative
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
