Varying fundamental constants: a full covariant approach and
  cosmological applications
  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.
