Equivalence Principle and Machian origin of extended gravity

TL;DR

This paper discusses the foundational aspects of extended gravity theories, emphasizing the importance of the Equivalence Principle and Machian ideas, and explores how direct coupling in these theories can reproduce MOND-like behavior.

Contribution

It introduces a framework where direct Ricci-matter coupling explains non-geodesic motion and recovers MOND-like theories at low energies, linking foundational principles with modified gravity.

Findings

Direct Ricci-matter coupling fixes inertial and gravitational mass ratio.

The framework reproduces MOND-like behavior at low energies.

Analysis supports the Machian origin of extended gravity theories.

Abstract

Chae's analyses on GAIA observations of wide binary stars have fortified the paradigm of extended gravity with particular attention to MOND-like theories. We recall that, starting from the origin of Einstein's general relativity, the request of Mach on the structure of the theory has been the core of the foundational debate. This issue is strictly connected with the nature of the mass-energy equivalence. This was exactly the key point that Einstein used to derive the same general relativity. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories, which have recently been further strengthened by analyses of GAIA observations, request a better understanding of the Equivalence Principle. By considering a direct coupling between the Ricci curvature scalar and the matter Lagrangian a non geodesic ratio between the inertial and the gravitational mass can be fixed and MOND-like theories are retrieved at low energies.