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Pierre Mourier (Lyon)

Spatial foliations and averaging in relativistic inhomogeneous cosmologies.

Évènements associés

  • Le jeudi 28 mars 2019 de 11:00 à 12:00

In the late-time Universe, the formation of small to large-scale matter structures leads to nonlinear regional deviations from the homogeneous and isotropic cosmological « background » models. This emergence of inhomogeneous structures may have a non-negligible « backreaction » effect on the global or large-scale expansion dynamics. A spatial averaging scheme for local scalar quantities may be used in order to describe such effects. In a general-relativistic, background-free picture, this is performed within a split of the model universe into three-dimensional spatial slices evolving in time, or « 3+1 » foliation of spacetime.

I will first introduce the spatial averaging and backreaction notions by recalling the results in the framework of an irrotational dust fluid model described in its (fluid-orthogonal) rest frames. I will then present generalizations of this scheme for the effective dynamics of a set of fluid elements for a general fluid source as seen in any 3+1 spatial foliation. The interest of an averaging procedure that focusses as much as possible on intrinsic properties of the fluid content will be highlighted, together with the example of a convenient and natural foliation choice that is itself built from the fluid flow. I will also show how the averaging formalism can be rewritten and extended under a manifestly covariant form and how this can be used for a more explicit study of the consequences of a change of foliation on the averages properties.