Orateur
Description
In the current era of precision cosmology, it is well-known that the present standard $\Lambda$CDM model, despite its successes, is an insufficient average of our actual Universe. Given the recorded tensions, it appears that a more precise representation of the local universe is mandatory. The Szekeres exact solution of General Relativity possesses all the nice properties allowing it to represent an inhomogeneous small scale universe becoming naturally homogeneous at some large transition scale. However, a raw use of the Szekeres model is challenging, since, besides a few constant parameters, it is described by a set of five metric functions, hence a difficult inference problem when we want to fit it to cosmological observations. However, a number of data analyses displayed in the recent literature have lead to the conclusion that the matter distribution and expansion are anisotropic roughly in the direction of the CMB dipole. This can be represented by the Szekeres axially symmetric version where two defining functions vanish. However, the inference issue remains even if reduced to three functions. To simplify such a fitting issue, we propose to replace this difficult inference problem by a spectral approximation problem and to use truncated Chebyshev polynomial expansions of the metric functions. As a first step, a truncation of the expansion at order two implies that a given Szekeres model can be determined by only nine constant parameters which greatly simplifies the fitting to observations. Moreover, beyond the transition to homogeneity, the $\Lambda$CDM model applies and the early universe picture is unchanged.