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

Konstantin G. Zloshchastiev
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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.

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Konstantin G. Zloshchastiev. 2006-06-25. Why do we live in a 4D world: Can cosmology, black holes and branes give an answer?. https://doi.org/10.1016/j.physletb.2006.05.034

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