Hypothesis of the dual relation between the Planck length and Metagalaxy size before the Big Bang

The hypothesis of the relation between the Planck length and the initial size of the Metagalaxy shaped as a de Sitter 3-sphere with the Planck density of sources (and with a curvature radius larger than the Planck length by twenty orders of magnitude) is proposed in the spirit of T-duality of string cosmology. This relation is taken with respect to the hypothetical sub-Planck fundamental length scale (exceeding the Planck scale by ten orders ofmagnitude). The hypothesis of the same dual relation between the grand unification scale and theHiggs boson size is also proposed.