Investigation of arbitrary large spatial dimensions in anisotropic Bianchi Type-I cosmologies with variable gravitational and cosmological parameters

In order to highlight time-varying constants such as the universal gravitation constant and to elucidate the effects of higher dimensions on cosmological parameters in the universe, we developed a toy cosmological model based upon an anisotropic n-dimensional spatial universe within an (n + 1)-dimensional spacetime. A dynamical power law model for dark energy is considered. The observational parameters of this cosmology are predicted and discussed. Considerable attention is devoted to the application of the extra-dimensional n-dimensional anisotropic cosmology model resulting in a universe consistent with current observations.