MOND as a peculiar case of the SIV theory

TL;DR

The paper explores the Scale Invariant Vacuum (SIV) theory, showing it aligns with MOND in weak fields, depends on universe properties, and offers an alternative to dark matter while predicting accelerated cosmic expansion.

Contribution

It demonstrates that SIV theory generalizes MOND, relates the a0 parameter to universe conditions, and provides a framework consistent with accelerated expansion without dark matter.

Findings

SIV reduces to MOND in the weak field limit.

The a0 parameter varies with universe density and age.

SIV predicts accelerated cosmic expansion.

Abstract

The scale invariant theory is preserving the fundamental physical properties of General Relativity, while enlarging the group of invariances subtending gravitation theory (Dirac1973; Canuto et al.1977). The Scale Invariant Vacuum (SIV) theory assumes, as gauging condition, that:"The macroscopic empty space is scale invariant, homogeneous and isotropic". Some basic properties in Weyl's Integrable Geometry and cotensor calculus are examined in relation with scalar-tensor theories. Possible scale invariant effects are strongly reduced by matter density, both at the cosmological and local levels. The weak feld limit of SIV tends to MOND, when the scale factor is taken as constant, an approximation valid (<1%) over the last 400 Myr. A better understanding of the a0-parameter is obtained: it corresponds to the equilibrium point of the Newtonian and SIV dynamical acceleration. Parameter a0 is not a universal constant, it depends on the density and age of the Universe. As MOND is doing, SIV theory avoids the call to dark matter, moreover the cosmological models predict accelerated expansion.