Abstract
The Universe was extremely homogeneous and isotropic at the beginning, as shown by the cosmic microwave background. Today, however, the major structures are highly contrasted. Could these structures have an effect on the dynamics of space-time? This phenomenon is known as " back-reaction ". To describe the Universe, we assume homogeneity, a "smooth" Universe based on an average density, which enables us to calculate the metric and define the geometry of the Universe. Einstein's equations link the geometry of the Universe to its content in matter density and momentum. But there's no commutativity between the application of these equations and averaging; Einstein's equations are non-linear. Some have tried to calculate the influence of back-reaction and show that it could lead to an accelerated expansion of the Universe, even from a fluid with positive or zero pressure. The advantage of this model is that it would not be necessary to add a fifth force, and this would explain why dark energy has only recently become dominant, when structures become highly contrasted. Nambu-Tanimoto's 2005 toy model, based on a small test sphere, was promising. But since then, Green and Wald (2011, 2016) have shown with more sophisticated calculations that the effect would be negligible. The debate remains open, for lack of an ultimate quantification. Many tests are possible, and galaxy clusters provide several, as do baryonic acoustic oscillations (BAOs), gravitational lenses and so on.
Locally, the local cosmic flows of structures are beginning to be well known, notably our 600 km/s motion towards the great attractor, a supercluster of galaxies behind the Milky Way. Yet we are unable to converge on a common dipole with the cosmic microwave background, and a residual cosmic flow of 200 km/s exists. Clusters of galaxies, with the SZ effect known from microwaves, and X-ray emissions also enable us to determine distances, and lift degeneracies with the cosmological background.
