Rethinking the link between matter and geometry

Abstract

In the present manuscript, I examine an intriguing relation at the classical level between general relativity and a theory where matter couples uniquely multiplicatively to geometry in the Lagrangian density. Interestingly, the gravitational constant $G$ is replaced by a novel fundamental constant, whose value is not tied to any classical phenomenon; while the value of $G$ itself becomes related to the dynamics of the universe. I concentrate on different aspects of the Equivalence Principle, as the theory is expected to violate all of its different formulations.

5 pages. Comments are welcome. v3: few cosmetic changes. Published version

References in corpus (4)

• f(R,L_m) gravity
• Equivalence Principle Violations and Couplings of a Light Dilaton
• Breaking of the equivalence principle in the electromagnetic sector and its cosmological signatures
• Late-time cosmology of scalar-tensor theories with universal multiplicative coupling between the scalar field and the matter Lagrangian