Integrable cosmological models in DD and variations of fundamental constants

Discovery of present acceleration of the Universe, dark matter and dark energy problems are great challenges to modern physics, which may bring to a new revolution. Integrable multidimensional models of gravitation and cosmology make up one of the proper approaches to study basic issues and, in particular, strong field objects, the Early and present Universe and black hole physics 1,2. Problems of the absolute G measurements and its possible time and range variations, which are reflections of the unification problem are discussed. A need for further measurements of G and its possible variations (also in space) is pointed out.