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Nonideal self-gravity and cosmology: the importance of correlations in the dynamics of the large-scale structures of the Universe

Inspired by the role of correlations in the statistical mechanics of nonideal self-interacting fluids, we suggest that unresolved sub-structures (i.e. correlations) have to be taken into account in the Virial theorem of self-gravitating astrophysical systems. We demonstrate that their omission leads to a missing mass problem by using the semi-analytic polytropic solutions of the Lane-Emden equation. This problem suggests to extend the Friedmann equations to the nonideal regime by taking into account correlations in the dynamics of the expansion. The increase of correlations induced by the formation of the large-scale structures could explain naturally the accelerated expansion of the Universe in such a paradigm.