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The manuscript studies a 3+N+1-dimensional space in which the N extradimensions are dynamically compact. The 3 large dimensions, behaving as thespacial part of the FRW metric, possess a different scale factor in comparisonwith the N extra ones, making the whole space anisotropic. The possible effectscaused by the existence of a common time-like coordinate between the compactdimensions and our 3-dimensional hypersurface are investigated. The higherdimensional Friedmann-Like equations of the mentioned model are achieved. Thecontinuity equation is reached at the special case of 3+4+1-dimensional metric.It is shown that not only the existence of the extra dimensions itself but alsothe pressure difference between the 3-dimensional hypersurface and the compactdimensions might get probed on the hypersurface as an additive source ofgravity with the same behavior as baryonic matter. Furthermore, the relationbetween the coupling constant of the higher-dimensional universe and theNewton's constant of gravitation is investigated to reach an estimated limitfor it. As another aim, the literature studies the role of dimensionality onthe behavior of the higher-dimensional Friedmann equations.

Solutions of Einstein Field Equation for an Extra-Dimensional Anisotropic Metric with Two Scale Factors