UDC 3937 On Multidimensional Cosmology with Anisotropic Fluid: Asymptotical Acceleration and Zero Variation of G A. G. Pakhomov Institute of Gravitation and Cosmology Peoples’ Friendship University of Russia 6, Miklukho-Maklaya str., Moscow, Russia, 117198 A multidimensional cosmological model describing the dynamics of n+1 flat factor-spaces with w0 > 1, the second one may contain phantom matter with w0 < −1. <...> It is shown that these solutions are special case of more general solutions with accelerated expansion of our 3-space M0 and asymptotically zero variation of the gravitational constant G. The model of an ideal many-dimensional substance with three isotropic dimensions of our space, additional dimensions and time is considered. <...> It is shown, that association of dynamic parameters of our three-dimensional space on additional dimensions in the open view may be expressed through coefficient of anisotropy of additional dimensions. <...> Dependence from parameter of an equation of state of our isotropic 3-dimensional space to coefficient of anisotropy of the additional dimensions, requiring the accelerated expansion of the Universe is received in an explicit aspect. <...> Key words and phrases: multidimensional gravitation, anisotropic fluid, accelerated expansion, variation of G. 1. <...> Introduction This paper deals with a possible temporal variation of gravitational constant G. This problem arose due to papers of Milne (1935) and Dirac (1937). <...> In Russia, these ideas were developed in the 60s and 70s by K.P. Staniukovich [1, 2], who was the first to consider simultaneous variations of several fundamental constants. mal scalar field [3] gave ˙G/G at the level of 10−11 −10−13 per year. <...> The calculations in string-like [4] and multidimensional models with perfect fluid [5] led to the level The first calculations based on general relativity with a perfect fluid and a confor10−12, those based on a general class of scalar-tensor theories [6] and simple multidimensional model with branes [7, 8] led for the present values of cosmological parameters 10−13 − 10−14 and 10−13 per year, respectively. <...> Similar estimations were made by Miyazaki within Machian theories [9] giving for ˙G/G the estimate 10−13 per year and by Fujii — on the level 10−14 −10−15 per year [10]. <...> Analysis of one more multidimensional <...>