  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.
