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Inspired by the role of correlations in the statistical mechanics of nonidealself-interacting fluids, we suggest that unresolved sub-structures (i.e.correlations) have to be taken into account in the Virial theorem ofself-gravitating astrophysical systems. We demonstrate that their omissionleads to a missing mass problem by using the semi-analytic polytropic solutionsof the Lane-Emden equation. This problem suggests to extend the Friedmannequations to the nonideal regime by taking into account correlations in thedynamics of the expansion. The increase of correlations induced by theformation of the large-scale structures could explain naturally the acceleratedexpansion of the Universe in such a paradigm.

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