Multidimensional models, dark energy and fundamental constants

Main problems of modern physics, gravitation, cosmology and fundamental constants in particular are discussed. Exact solutions with an exponential and power-law behaviors of scale factors in various models (with perfect fluids, branes) are considered. The metric is defined on the manifold containing a product of several n+1 Ricci-flat factor spaces. Solutions with accelerated expansion of our 3-space M0 and a small enough variation of the effective gravitational constant G consistent with present observational and experimental data are given. © 2009 American Institute of Physics.