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

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

2001-01-17

arxiv.org/abs/gr-qc/0101070v1

General Relativity, Cosmology, and Gravitational Lensing, G. Marmo, C. Rubano and P. Scudellaro (eds.), Napoli Series on Physi

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LateX 15 pages, to be published in: Proc. `General Relativity, Cosmology, and Gravitational Lensing', (meeting in memory of R.

Scientific paper

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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