Why do we live in a 4D world: Can cosmology, black holes and branes give an answer?
arXiv:hep-th/0601221 · doi:10.1016/j.physletb.2006.05.034
Abstract
We derive the general form of the cosmological scalar field potential which is compatible both with the existence of black holes and p-branes related to string/M theory and with multidimensional inflationary cosmology. It is shown that the scalar potential alters non-trivially from dimension to dimension yet always obeys one single equation where the number of spacetime dimensions is a free parameter. Using this equation we formulate an eigenvalue problem for the dimensionality parameter. It turns out that in the low-energy regime of sub-Planckian values of the inflaton field, i.e., when the Universe has cooled and expanded sufficiently enough, the value four arises as the largest admissible (eigen)value of this parameter.
5 pages, REVTeX 4. Updates: v3: eq (4) corrected, more refs added; v4(final): appendix added