Averaging Problem

  1. Ellis G F R: Relativistic cosmology: Its nature, aims and problems General Relativity and Gravitation (Invited Papers and Discussion Reports of the 10th International Conference), ed. B Bertotti, F de Felice and A Pascolini (Dordrecht: Reidel, 1984), 215
  2. Ellis G F R, W Stoeger: The `Fitting Problem' in Cosmology, Class. Quantum Grav. 4 (1987), 1697
  3. Futamase T: Approximation Scheme for Constructing a Clumpy Universe in General Relativity, Phys. Rev. Lett. 61 (1988), 2175
  4. Bildhauer S, T Futamase: The Age Problem in Inhomogeneous Universes, Gen. Rel. Grav. 23 (1991), 1251
    NB: Very good!!! Problem well exposed, transparent explanation of proposed solution Ansatz. Modifies the Friedmann equation by taking backreactions of inhomogeneities on the expansion rate into account. Sub-Hubble radius scale inhomogeneities are modelled in Newtonian terms and a Zel'dovich approximation to first order is applied. The spatial curvature is assumed to average to zero, $k=0$.
  5. Zalaletdinov R M: Averaging out the Einstein Equations, Gen. Rel. Grav. 24 (1992), 1015
  6. Zotov N V, W R Stoeger SJ: Averaging Einstein's Equations, Class. Quantum Grav. 9 (1992), 1023
    NB: Refers to Ellis G F R in: General Relativity And Gravitation, ed B Bertotti, Reidel, Dordrecht 1984.
  7. Kasai M: Inhomogeneous Cosmological Models which are Homogeneous and Isotropic on Average, Phys. Rev. D 47 (1993), 3214
    NB: Irrotational dust in comoving description. Applies spatial averaging (of the energy density, etc) in terms of the physical 3-metric on the 3-surfaces of (synchronous) constant time. Discusses a one-dimensional collapse sub-solution of the Szekeres class as an example of a relativistic version of the Zel'dovich approximation in Newtonian cosmology.
  8. Zalaletdinov R M: Towards a Theory of Macroscopic Gravity, Gen. Rel. Grav. 25 (1993), 673.
  9. Zalaletdinov R M: Averaging Problem in General Relativity, Macroscopic Gravity and Using Einstein's Equations in Cosmology, Preprint gr-qc/9703016
  10. Boersma J P: Averaging in Cosmology, Phys. Rev. D 57 (1998), 798. Also: Preprint gr-qc/9711057.
  11. Tanimoto M: Criticality and Averaging in Cosmology, Prog. Theor. Phys. 102 (1999), 1001. Also: Preprint gr-qc/9907103.
    NB: Deviations of closed/compact spatially inhomogeneous dust cosmologies from the FLRW case; comoving, synchronous description; total spatial volume as central dynamical variable.
  12. Buchert T: On Average Properties of Inhomogeneous Fluids in General Relativity I: Dust Cosmologies, Gen. Rel. Grav. 32 (2000), 105. Also: Preprint gr-qc/9906015.

Selected References
Last revision: Mon, 21-8-2000 (This page is under construction)