Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inhomogeneities in the Universe and the Fitting Problem   Observational cosmology provides us with a large number of high precision
data which are used to derive models trying to reproduce ``on the mean'' our
observable patch of the Universe. Most of these attempts are achieved in the
framework of a Friedmann-Lema\^itre cosmology where large scale homogeneity is
assumed. However, we know, from the observation of structures at increasing
scales, that these models are only approximations of a smoothed or averaged
inhomogeneous underlying patern. Anyhow, when modelling the Universe, the usual
method is to use continuous functions representing the kinematical scalars of
the velocity field, implicitly assuming that they represent volume averages of
the corresponding fine-scale inhomogeneous quantities, then put them into the
Einstein equations which are solved to give the model and its dependance upon a
number of parameters arbitrarily defined. In General Relativity, such a method
is very much involved since the equations which determine the metric tensor and
the quantities calculated from it are highly nonlinear. The question raised by
the method consisting of determining the parameters of an a priori assumed FLRW
model from observational data is the ``fitting problem'' brought to general
attention by Ellis and Stoeger in the 80's. This problem has recently
experienced a reniewed attention due to the amount of available data and the
increase of the minimum scale at which homogeneity can be assumed. We propose a
discussion of this issue in the light of the latest developments of
observational and theoretical cosmology.

15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int