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Abstract: Observational cosmology provides us with a large number of high precisiondata which are used to derive models trying to reproduce ``on the mean- ourobservable patch of the Universe. Most of these attempts are achieved in theframework of a Friedmann-Lema\^itre cosmology where large scale homogeneity isassumed. However, we know, from the observation of structures at increasingscales, that these models are only approximations of a smoothed or averagedinhomogeneous underlying patern. Anyhow, when modelling the Universe, the usualmethod is to use continuous functions representing the kinematical scalars ofthe velocity field, implicitly assuming that they represent volume averages ofthe corresponding fine-scale inhomogeneous quantities, then put them into theEinstein equations which are solved to give the model and its dependance upon anumber of parameters arbitrarily defined. In General Relativity, such a methodis very much involved since the equations which determine the metric tensor andthe quantities calculated from it are highly nonlinear. The question raised bythe method consisting of determining the parameters of an a priori assumed FLRWmodel from observational data is the ``fitting problem- brought to generalattention by Ellis and Stoeger in the 80-s. This problem has recentlyexperienced a reniewed attention due to the amount of available data and theincrease of the minimum scale at which homogeneity can be assumed. We propose adiscussion of this issue in the light of the latest developments ofobservational and theoretical cosmology.

Autor: Marie-Noëlle Célérier Observatoire de Paris-Meudon


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