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We show that, as a result of non-linear self-interactions, it is feasible, atleast in light of the bounds coming from terrestrial tests of gravity,measurements of the Casimir force and those constraints imposed by the physicsof compact objects, big-bang nucleosynthesis and measurements of the cosmicmicrowave background, for there to exist, in our Universe, one or more scalarfields that couple to matter much more strongly than gravity does. These scalarfields behave like chameleons: changing their properties to fit theirsurroundings. As a result these scalar fields can be not only very stronglycoupled to matter, but also remain relatively light over solar system scales.These fields could also be detected by a number of future experiments providedthey are properly designed to do so. These results open up an altogether newwindow, which might lead to a completely different view of the role played bylight scalar fields in particle physics and cosmology.Comment: 72 pages, 13 figures. New section on the Casimir Effect and  experimental tests. Tighther constraints on the models have now been  obtained. Sections of the mathematical formalism and experimental bounds were  re-written and clarified. Number of pages reduced due to revtex4 forma

Evading equivalence principle violations, cosmological, and other experimental constraints in scalar field theories with a strong coupling to matter