The evidence for the accelerated expansion of the universe and the time-dependence of the fine-structure constant suggests the existence of at least one scalar field with a mass of order H_0. If such a field exists, then it is generally assumed that its coupling to matter must be tuned to unnaturally small values in order to satisfy the tests of the Equivalence Principle (EP). In this paper, we present an alternative explanation which allows scalar fields to evolve cosmologically while having couplings to matter of order unity. In our scenario, the mass of the fields depends on the local matter density: the interaction range is typically of order 1 mm on Earth (where the density is high) and of order 10-10^4 AU in the solar system (where the density is low). All current bounds from tests of General Relativity are satisfied. Nevertheless, we predict that near-future experiments that will test gravity in space will measure an effective Newton's constant different by order unity from that on Earth, as well as EP violations stronger than currently allowed by laboratory experiments. Such outcomes would constitute a smoking gun for our scenario.

25 pages, 5 figures. v2: Minor modifications and updated references