Varying fundamental constants: a full covariant approach and cosmological applications

Abstract: We build a minimal extension of General Relativity in which Newton's gravitational coupling, $G$, the speed of light, $c$, and the cosmological constant, $\Lambda$, are spacetime variables. This is done while satisfying the contracted Bianchi identity as well as the local conservation of energy momentum tensor. A dynamical constraint is derived, which shows that variations of $G$ and $c$ are coupled to the local matter-energy physical content, while variation of $\Lambda$ is coupled to the local geometry. This constraint presents a natural cosmological screening mechanism that brings new perspective concerning the current observations of a cosmological constant, $\Lambda_0$ in cosmological observations. We also explore early universe background cosmology and show that the proposal provides alternatives to obtain an accelerated expansion, similar to those coming from Varying Speed of Light theories.