Newtonian-like gravity with variable $G$

TL;DR

This paper introduces a dynamical theory of gravity where the gravitational constant G varies naturally from the theory's internal structure, extending Newtonian gravity inspired by Brans-Dicke theory, with applications to static, spherical, and cosmological scenarios.

Contribution

It develops a Lagrangian formulation for a variable G gravity theory where G's evolution is intrinsic, not imposed, inspired by Brans-Dicke gravity.

Findings

G varies naturally within the theory's framework.

The theory describes static, spherically symmetric, and cosmological solutions.

The model aligns with known gravitational phenomena in these regimes.

Abstract

We propose a Lagrangian formulation for a varying $G$ Newtonian-like theory inspired by the Brans-Dicke gravity. Rather than imposing an {\it ad hoc} dependence for the gravitational coupling, as previously done in the literature, in our proposal the running of $G$ emerges naturally from the internal dynamical structure of the theory. We explore the features of the resulting gravitational field for static and spherically symmetric mass distributions as well as within the cosmological framework.