A&A 434, 45-52 (2005)
Cosmological effects in the local static frameM. Mizony1 and M. Lachièze-Rey2
1 Institut Girard Desargues, CNRS UMR 5028, Bâtiment Jean Braconnier, Département de mathématiques, Université Lyon I, 43 boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
2 Service d'Astrophysique, CE Saclay, 91191 Gif-sur-Yvette Cedex, France CNRS FRE K25910 "Plasmas, Gravitation et Cosmologie"
(Received 18 October 2004 / Accepted 13 December 2004 )
What is the influence of cosmology (the expansion law and its acceleration, the cosmological constant...) on the dynamics and optics of a local system like the solar system, a galaxy, a cluster or a supercluster? The answer requires the solution of the Einstein equation with the local source, which tends towards the cosmological model at large distances. There is, in general, no analytic expression for the corresponding metric, but we calculate here an expansion in a small parameter, which allows us to answer this question. First, we derive a static expression for the pure cosmological (Friedmann-Lemaître) metric, whose validity, although local, extends in a very large region around the observer. This expression appears as the metric of an osculating de Sitter model.
Key words: gravitation -- relativity -- galaxies: kinematics and dynamics -- cosmology: theory
© ESO 2005