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Quantum Stability of Chameleon Field Theories

Chameleon scalar fields are dark energy candidates which suppress fifth forces in high density regions of the universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound $m < 0.0073 (ρ/ 10 {\rm g\, cm}^{-3})^{1/3}$eV for gravitational strength coupling whereas fifth force experiments place a lower bound of $m>0.0042$\,eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well-controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential.