A scenario for the dimensional compactification in eleven-dimensional space-time

We discuss the inhomogeneous multidimensional mixmaster model in view of the appearing, near the cosmological singularity, of a scenario for the dimensional compactification in correspondence to an 11-dimensional space-time. Our analysis candidates such a collapsing picture toward the singularity to describe the actual expanding 3-dimensional Universe and an associated collapsed 7-dimensional space. To this end, a conformal factor is determined in front of the 4-dimensional metric to remove the 4-curvature divergences and the resulting Universe expands with a power-law inflation. Thus we provide an additional peculiarity of the eleven space-time dimensions in view of implementing a geometrical theory of unification.