Gravity and cosmology as key problems of the millennium

Discovery of present acceleration of the Universe, dark matter and dark energy problems are also a great challenge to modern physics, which may bring to a new revolution. Gravitation as a fundamental interaction that governs all phenomena at large and very small scales, but still not well understood at a quantum level, is a missing cardinal link to unification of all physical interactions.Integrable multidimensional models of gravitation and cosmology make up one of the proper approaches to study basic issues and strong field objects, the Early and present Universe and black hole physics in particular [1,2]. Problems of the absolute G measurements and its possible time and range variations are reflections of the unification problem. The choice, nature, classification and precision of determination of fundamental physical constants are described. The problem of their temporal variations is also discussed, temporal and range variations of G in particular. A need for further measurements of G, its possible variations is pointed out. The novel gravitational multipurpose space project SEE, aimed for measuring G and its stability in space and time 3-4 orders better than at present, may answer many important questions posed by gravitation, cosmology and unified theories © 2006 American Institute of Physics.