Effect of a scale-dependent cosmological term on the motion of small test particles in a Schwarzschild background

TL;DR

This paper investigates how a scale-dependent cosmological term modifies the gravitational field around a spherical mass, leading to tiny non-Newtonian effects that could influence spacecraft trajectory analyses.

Contribution

It introduces a simple model of a scale-dependent cosmological term and computes its effect on the Schwarzschild metric, revealing a small correction to the gravitational potential.

Findings

Identifies a tiny non-Newtonian component in the gravitational potential.

Suggests potential relevance for Pioneer spacecraft data analysis.

Abstract

It was recently suggested that the gravitational action could contain a scale-dependent cosmological term, depending on the length or momentum scale characteristic of the processes under consideration. In this work we explore a simple possible consequence of this assumption. We compute the field generated in empty space by a static spherical source (the Schwarzschild metric), using the modified action. The resulting static potential turns out to contain a tiny non-Newtonian component which depends on the size of the test particles. The possible relevance of this small correction for the analysis of the recent Pioneers data [J.D. Anderson et al., Phys. Rev. Lett. 81 (1998) 2858] is briefly discussed.