Marc Lachieze-Rey

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-Lemaˆotre) 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,

Orbifold construction of the modes of the Poincaré dodecahedral space

We provide a new construction of the modes of the Poincare dodecahedral space S3/I*. The construction uses the Hopf map, Maxwells multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S3/I*, shedding new light on the geometrical significance of the dimension of each space of k-modes, as well as on the modes themselves.

Functions on the Sphere and multipole vectors

It has recently been suggested to represent functions on the sphere by a “ multipole vector decomposition ”, rather than by the usual spherical harmonic expansion. I recall the definition and main properties of the multipole vectors, as they were introduced in the literature. I show that they are related to the harmonic projection and to the Maxwell decomposition. This allows to deduce additional properties. I extend to complex polynomials.

Dark Matter Distribution in X-Ray Clusters of Galaxies

The presence of highly peaked cluster cores consisting of dark matter is well supported by observations, modelling and a qualitative physical model.