Cosmological effects in the local static frame

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, a supercluster...? The answer requires the solution of Einstein equation with the local source, which tends towards the cosmological model at large distance. There is, in general, no analytic expression for the corresponding metric, but we calculate here an expansion in a small parameter, which allows to answer the question. First, we derive a static expression for the pure cosmological (Friedmann-Lema\^itre) metric, whose validity, although local, extends in a very large neighborhood of the observer. This expression appears as the metric of an osculating de Sitter model. Then we propose an expansion of the cosmological metric with a local source, which is valid in a very large neighborhood of the local system. This allows to calculate exactly the (tiny) influence of cosmology on the dynamics of the solar system: it results that, contrary to some claims, cosmological effects fail to account for the unexplained acceleration of the Pioneer probe by several order of magnitudes. Our expression provide estimations of the cosmological influence in the calculations of rotation or dispersion velocity curves in galaxies, clusters, and any type of cosmic structure, necessary for precise evaluations of dark matter and/or cosmic flows. The same metric can also be used to estimate the influence of cosmology on gravitational optics in the vicinity of such systems.Comment: to appear in Astron. & Astrop

De Sitter Waves and the Zero Curvature Limit

We show that a particular set of global modes for the massive de Sitter scalar field (the de Sitter waves) allows to manage the group representations and the Fourier transform in the flat (Minkowskian) limit. This is in opposition to the usual acceptance based on a previous result, suggesting the appearance of negative energy in the limit process. This method also confirms that the Euclidean vacuum, in de Sitter spacetime, has to be preferred as far as one wishes to recover ordinary QFT in the flat limit.Comment: 9 pages, latex no figure, to appear in Phys. Rev.

Cosmological expansion and local systems: a Lema\^{i}tre-Tolman-Bondi model

We propose a Lema\^{i}tre-Tolman-Bondi system mimicking a two-body system to address the problem of the cosmological expansion versus local dynamics. This system is strongly bound but participates in the cosmic expansion and is exactly comoving with the cosmic substratum