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A mechanism to control the cosmological constant through a scalar fieldnon-minimally coupled to gravity is proposed. By utilizing non-minimal phantomor quintessence, the cosmological constant, which may be large originally, canbe automatically driven to a value on the scale of the mass parameter in thephantom/quintessence potential V(phi). The reduction of a large cosmologicalconstant involves the weakening of gravity that therefore may be much strongerinitially. There exist the cases where originally gravity is on the TeV scaleso that the hierarchy between gravity and three gauge interactions in thestandard model of particle physics is bridged at the beginning. Although thecosmological constant can be automatically tuned or largely reduced under thismechanism, its energy density may still remain on the same order of magnitudeas the original one. Thus, explaining the smallness of theobservation-suggested cosmological constant energy density is still a difficultmission yet to be completed.

Automatic Control over the Cosmological Constant through Non-minimal Phantom and Quintessence