Cosmological effects in the local static frame

TL;DR

This paper develops an expansion method to evaluate the influence of cosmological effects on local systems' dynamics and optics, providing precise estimates relevant for dark matter, cosmic flows, and gravitational lensing.

Contribution

It introduces a new expansion approach for the cosmological metric with local sources, enabling accurate assessment of cosmological effects on local astrophysical phenomena.

Findings

Cosmological effects on the solar system are negligible for the Pioneer anomaly.

The method estimates cosmological influence on galaxy rotation curves.

The approach aids in precise calculations of gravitational optics near cosmic structures.

Abstract

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.