A Machian Request for the Equivalence Principle in Extended Gravity and non-geodesic motion

TL;DR

This paper explores the foundational aspects of the Equivalence Principle within extended gravity theories, proposing a direct coupling between Ricci curvature and matter to explain non-geodesic motion and recover Milgrom acceleration.

Contribution

It introduces a novel coupling between Ricci scalar and matter Lagrangian, addressing the EP in extended gravity and deriving Milgrom acceleration at low energies.

Findings

A non-geodesic ratio m_{i}/m_{g} can be fixed.

Milgrom acceleration is recovered at low energies.

Provides insights into the nature of EP in extended gravity theories.

Abstract

Starting from the origin of Einstein general relativity (GR) the request of Mach on the theory's structure has been the core of the foundational debate. That problem is strictly connected with the nature of the mass-energy equivalence. It is well known that this is exactly the key point that Einstein used to realize a metric theory of gravitation having an unequalled beauty and elegance. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories request a better understanding of Equivalence Principle (EP). The MOND theory by Milgrom proposes a modification of Newtonian dynamics and we consider a direct coupling between the Ricci curvature scalar and the matter Lagrangian showing that a non geodesic ratio m_{i}/m_{g} can be fixed and that Milgrom acceleration is retrieved at low energies.