The fate of four dimensions
Abstract
In gravitational theories with extra dimensions, it is argued that the existence of a positive vacuum energy generically implies catastrophic instability of our fourdimensional world. The most generic instability is a decompactification transition to growth of the extra dimensions, although other equally bad transitions may take place. This follows from simple considerations based on the form of the potential for the size modulus of the extra dimensions, and apparently offers a resolution of the conundrums presented by eternal de Sitter space. This argument is illustrated in the context of string theory with a general discussion of potentials generated by fluxes, wrapped branes, and stringy corrections. Moreover, it is unlikely that the present acceleration of the Universe represents an ongoing transition in a quintessence scenario rolling toward decompactification, unless the higherdimensional theory has a cosmological constant.
 Publication:

Physical Review D
 Pub Date:
 July 2003
 DOI:
 10.1103/PhysRevD.68.026006
 arXiv:
 arXiv:hepth/0303031
 Bibcode:
 2003PhRvD..68b6006G
 Keywords:

 11.25.Mj;
 04.50.+h;
 98.80.Cq;
 98.80.Jk;
 Compactification and fourdimensional models;
 Gravity in more than four dimensions KaluzaKlein theory unified field theories;
 alternative theories of gravity;
 Particletheory and fieldtheory models of the early Universe;
 Mathematical and relativistic aspects of cosmology;
 High Energy Physics  Theory;
 Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 17 pages, harvmac. v.2: minor improvements