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

A mechanism to control the cosmological constant through a scalar field non-minimally coupled to gravity is proposed. By utilizing non-minimal phantom or quintessence, the cosmological constant, which may be large originally, can be automatically driven to a value on the scale of the mass parameter in the phantom/quintessence potential V(phi). The reduction of a large cosmological constant involves the weakening of gravity that therefore may be much stronger initially. There exist the cases where originally gravity is on the TeV scale so that the hierarchy between gravity and three gauge interactions in the standard model of particle physics is bridged at the beginning. Although the cosmological constant can be automatically tuned or largely reduced under this mechanism, its energy density may still remain on the same order of magnitude as the original one. Thus, explaining the smallness of the observation-suggested cosmological constant energy density is still a difficult mission yet to be completed.