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Matter seen at many scales and the geometry of averaging in relativistic cosmology

Thomas Buchert·Mauro Carfora
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Abstract

We investigate the scale-dependence of Eulerian volume averages of scalar functions on Riemannian three-manifolds. We propose a complementary view of a Lagrangian scaling of variables as opposed to their Eulerian averaging on spatial domains. This program explains rigorously the origin of the Ricci deformation flow for the metric, a flow which, on heuristic grounds, has been already suggested as a possible candidate for averaging the initial data set for cosmological spacetimes.

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Thomas Buchert, Mauro Carfora. 2001-01-17. Matter seen at many scales and the geometry of averaging in relativistic cosmology. https://arxiv.org/abs/gr-qc/0101070

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