Zhuk, Alexander2010-08-192010-08-192007Astronomical & Astrophysical Transactions. The Journal of the Eurasian Astronomical Society1055-6796 print1476-3540 onlinehttps://dspace.onu.edu.ua/handle/123456789/79We investigate the possibility of the construction of the conventional Friedmann cosmology for our observable Universe if the underlying theory is the multidimensional Kaluza–Klein model.We show that the effective Friedmann model obtained by dynamic compactification of the multidimensional model is faced with too strong variations in the fundamental constants. On the other hand, models with stable compactification of the internal space are free from this problem and also result in conventional four-dimensonal cosmological behaviour for our Universe. We prove a no-go theorem, which shows that stable compactification of the internal spaces is possible only if the equations of state in the external and internal spaces are properly adjusted to each other. With a proper choice of parameters (fine tuning), the effective cosmological constant in this model provides the late-time acceleration of the Universe.enMultidimensional cosmological modelsDynamic compactificationStable compactificationFundamental constant variationArticle