[Paper Review] On the influence of the global cosmological expansion on the local dynamics in the Solar System

Matteo Carrera, Domenico Giulini|ArXiv.org|Feb 24, 2006

Cosmology and Gravitation Theories46 references14 citations

TL;DR

This paper investigates whether cosmic expansion influences local dynamics in the Solar System, particularly in relation to the Pioneer anomaly. Using Newtonian and relativistic models—including the McVittie metric and kinematical analysis—it finds that dynamical effects are negligible (suppressing any cosmological influence by 13 orders of magnitude), while kinematical effects, though theoretically present, are also far too small to explain the observed anomalous acceleration of ~10⁻⁹ m/s².

ABSTRACT

In this expository paper we address the question of whether, and to what extent, the cosmological expansion influences the dynamics on small scales (as compared to cosmological ones), particularly in our Solar System. We distinguish between dynamical and kinematical effects and critically review the status of both as presented in the current literature.

Motivation & Objective

• To assess whether the global expansion of the universe influences local gravitational dynamics in the Solar System.
• To evaluate the validity of claims linking the Pioneer anomaly to cosmological expansion effects.
• To distinguish between dynamical and kinematical effects of cosmic expansion on bound systems.
• To critically analyze the Hc-type kinematical effect proposed by Dicke and Peebles as a possible explanation for the Pioneer anomaly.
• To clarify the role of back-reaction effects of local inhomogeneities in cosmological data interpretation within General Relativity.

Proposed method

• Uses the McVittie metric to model a spherically symmetric mass in an expanding FRW universe, enabling a fully relativistic treatment of gravitationally bound systems.
• Applies the Schücking radius formalism to determine the boundary where local gravity dominates over cosmological expansion.
• Performs a kinematical analysis of local Einstein-simultaneity in isotropic cosmological spacetimes to assess apparent accelerations.
• Re-evaluates the Dicke-Peebles argument for an Hc-type kinematical effect, identifying a (v/c)³ suppression factor.
• Compares theoretical predictions with the observed Pioneer anomaly of ~10⁻⁹ m/s² to assess plausibility.
• Employs a structured literature review of over 80 references to contextualize current theoretical and observational status.

Experimental results

Research questions

• RQ1 Can the global cosmological expansion produce measurable dynamical effects on the orbital motion of planets and spacecraft in the Solar System?
• RQ2 To what extent do kinematical effects arising from cosmic expansion mimic an apparent acceleration in local inertial frames?
• RQ3 Is the Hc-type kinematical effect, proposed as an explanation for the Pioneer anomaly, consistent with relativistic dynamics?
• RQ4 How do back-reaction effects of local inhomogeneities influence the interpretation of cosmological observations?
• RQ5 What is the quantitative magnitude of cosmological influence on Solar System dynamics compared to the observed Pioneer anomaly?

Key findings

• Dynamical effects of cosmic expansion on the Solar System are negligible, suppressed by many orders of magnitude—far below the 10⁻⁹ m/s² level of the Pioneer anomaly.
• The McVittie metric confirms that within the Schücking radius, local dynamics remain unaffected by global expansion, as the vacuum solution remains Schwarzschild-like.
• Kinematical effects, though present, are suppressed by a factor of (v/c)³, reducing the Hc-type effect by 13 orders of magnitude for the Pioneer spacecrafts.
• The apparent acceleration from kinematical effects is therefore too small to explain the Pioneer anomaly, ruling out this mechanism as a primary cause.
• The paper concludes that while cosmological expansion does not significantly affect local dynamics, the back-reaction of inhomogeneities on cosmological observables remains an open and fundamental problem in General Relativity.
• The literature review highlights the lack of consensus and the need for a more rigorous, non-perturbative treatment of inhomogeneous cosmology in interpreting both local and global data.