Cosmology in the Solar System: Pioneer effect is not cosmological

TL;DR

This paper investigates whether cosmic expansion influences the Solar System and concludes that the Pioneer effect cannot be explained by cosmological effects, contradicting some previous claims.

Contribution

It provides a detailed relativistic analysis showing the negligible impact of cosmology on local gravitational systems like the Solar System.

Findings

Cosmological influence on the Pioneer effect is about 10 orders of magnitude too small.

The solution of Einstein equations with local and cosmological sources clarifies local dynamics.

Contradicts claims that cosmic expansion affects Solar System dynamics.

Abstract

Does the Solar System and, more generally, a gravitationally bound system follow the cosmic expansion law ? Is there a cosmological influence on the dynamics or optics in such systems ? The general relativity theory provides an unique and unambiguous answer, as a solution of Einstein equations with a local source in addition to the cosmic fluid, and obeying the correct (cosmological) limiting conditions. This solution has no analytic expression. A Taylor development of its metric allows a complete treatment of dynamics and optics in gravitationally bound systems, up to the size of galaxy clusters, taking into account both local and cosmological effects. In the solar System, this provides an estimation of the (non zero) cosmological influence on the Pioneer probe: it fails to account for the " Pioneer effect " by about 10 orders of magnitude. We criticize contradictory claims on this topic.