Cosmological Constant or Cosmological Potential

In the framework of a model of minimal of dilatonic gravity (MDG) with cosmological potential we consider: the relations of MDG with nonlinear gravity and string theory; natural cosmological units, defined by cosmological constant; the properties of cosmological factor, derived from solar system and Earth-surface gravitational experiments; universal anty-gravitational interactions, induced by positive cosmological constant and by Nordtved effect; a new formulation of cosmological constant problem using the ratio of introduced cosmological action and Planck constant $\sim {10}^{122}$;qualitative analysis of this huge number based on classical action of effective Bohr hydrogen atoms; inverse cosmological problem: to find cosmological potential which yields given evolution of the RW Universe; and comment other general properties of MDG.