Non-relativistic Extended Gravity and its applications across different astrophysical scales

TL;DR

This paper introduces an extended gravity model based on dimensional analysis that transitions between Newtonian and MOND-like regimes, aiming to explain dark matter phenomena without modifying dynamics.

Contribution

It proposes a new non-relativistic gravity extension grounded in fundamental constants, emphasizing force modifications over dynamical changes, to account for astrophysical observations.

Findings

Reproduces galaxy rotation curves without dark matter

Predicts phenomena typically attributed to dark matter

Unifies Newtonian and MOND regimes through dimensional analysis

Abstract

Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to Newton's gravity and to a MOND-like description in two different mass and length regimes. It is shown that a modification on the force sector (and not in the dynamical one as MOND does) is more convenient and can reproduce and predict different phenomena usually ascribed to dark matter at the non-relativistic level.