Why do we live in a 4D world: Can cosmology, black holes and branes give an answer?

Details Why do we live in a 4D world: Can cosmology, black holes and branes give an answer? Why do we live in a 4D world: Can cosmology, black holes and branes give an answer?

2006-01-30

arxiv.org/abs/hep-th/0601221v4

Phys.Lett. B638 (2006) 89-93

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, REVTeX 4. Updates: v3: eq (4) corrected, more refs added; v4(final): appendix added

Scientific paper

10.1016/j.physletb.2006.05.034

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.

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