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A class of cosmological solutions of higher dimensional Einstein fieldequations with the energy-momentum tensor of a homogeneous, isotropic fluid asthe source are considered with an anisotropic metric that includes the directsum of a 3-dimensional (physical, flat) external space metric and ann-dimensional (compact, flat) internal space metric. A simple kinematicalconstraint is postulated that correlates the expansion rates of the externaland internal spaces in terms of a real parameter {\lambda}. A specific solutionfor which both the external and internal spaces expand at different rates isgiven analytically for n=3. Assuming that the internal dimensions were atPlanck length scales when the external space starts with a Big Bang (t=0), theyexpand only 1.49 times and stay at Planck length scales even in the present ageof the universe (13.7 Gyr). The effective four dimensional universe wouldexhibit a behavior consistent with our current understanding of the observeduniverse. It would start in a stiff fluid dominated phase and evolve throughradiation dominated and pressureless matter dominated phases, eventually goinginto a de Sitter phase at late times.

A four-dimensional {\Lambda}CDM-type cosmological model induced from higher dimensions using a kinematical constraint