Scale-invariant dynamics in the Solar System

TL;DR

The paper tests the scale-invariant dynamics (SID) theory as an alternative to dark matter, finding it incompatible with lunar laser ranging data and stellar age estimates, thus falsifying the theory.

Contribution

It provides a comprehensive observational test of SID, demonstrating its incompatibility with empirical data and challenging its viability as an alternative gravity model.

Findings

SID predicts Earth-Moon orbit expansion incompatible with laser ranging

SID implies older stellar ages inconsistent with standard cosmology

SID is falsified by observations across multiple scales

Abstract

The covariant scale-invariant dynamics (SID) theory has recently been proposed as a possible explanation for the observed dynamical discrepancies in galaxies (Maeder & Gueorguiev 2020). SID implies that these discrepancies $-$ commonly attributed to dark matter $-$ arise instead from a non-standard velocity-dependent force that causes two-body near-Keplerian orbits to expand. We show that the predicted expansion of the Earth-Moon orbit is incompatible with lunar laser ranging data at $>200\sigma$. Moreover, SID predicts that the gravitating mass of any object was much smaller in the past. If true, a low-mass red giant star must be significantly older than in standard theory. This would make it much older than the conventional age of the Universe, which however is expected to be similarly old in SID. Moreover, it is not completely clear whether SID truly contains new physics beyond General Relativity, with several previous works arguing that the extra degree of freedom is purely mathematical. We conclude that the SID model is falsified at high significance by observations across a range of scales, even if it is theoretically well formulated.