  The manuscript studies a 3+N+1-dimensional space in which the N extra
dimensions are dynamically compact. The 3 large dimensions, behaving as the
spacial part of the FRW metric, possess a different scale factor in comparison
with the N extra ones, making the whole space anisotropic. The possible effects
caused by the existence of a common time-like coordinate between the compact
dimensions and our 3-dimensional hypersurface are investigated. The higher
dimensional Friedmann-Like equations of the mentioned model are achieved. The
continuity 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 also
the pressure difference between the 3-dimensional hypersurface and the compact
dimensions might get probed on the hypersurface as an additive source of
gravity with the same behavior as baryonic matter. Furthermore, the relation
between the coupling constant of the higher-dimensional universe and the
Newton's constant of gravitation is investigated to reach an estimated limit
for it. As another aim, the literature studies the role of dimensionality on
the behavior of the higher-dimensional Friedmann equations.
