2002/10/31 by Thomas Buchert, Mauro Carfora · 104 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Astronomy #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Mathematical physics #Nuclear physics #Physics #Relativistic quantum chemistry #Scaling #Theoretical physics #astro-ph #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1088/0264-9381/19/23/314
published in Classical and Quantum Gravity 19(23), 6109-6145 (IOP Publishing) · LateX, IOPstyle, 48 pages, 11 figures; matches published version in C.Q.G
openalex publication_date 2002/11/11 · arxiv created 2002/11/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract. Averaged inhomogeneous cosmologies lie at the forefront of interest, since cosmological parameters like the rate of expansion or the mass density are to be considered as volume–averaged quantities and only these can be compared with observations. For this reason the relevant parameters are intrinsically scale–dependent and one wishes to control this dependence without restricting the cosmological model by unphysical assumptions. In the latter respect we contrast our way to approach the averaging problem in relativistic cosmology with shortcomings of averaged Newtonian models. Explicitly, we investigate the scale–dependence of Eulerian volume averages of scalar functions on Riemannian three–manifolds. We propose a complementary view of a Lagrangian smoothing of (tensorial) variables as opposed to their Eulerian averaging on spatial domains. This program is realized with the help of a global Ricci deformation flow for the metric. We explain rigorously the origin of the Ricci flow which, on heuristic grounds, has already been suggested as a possible candidate for smoothing the initial data set for cosmological spacetimes. The smoothing of geometry implies a renormalization of averaged spatial variables. We discuss the results in terms of effective cosmological parameters that would be assigned to the smoothed cosmological spacetime. In particular, we find that the on the smoothed spatial domain B evaluated cosmological parameters obey Ω m