Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-10-11
Nucl.Phys.B709:213-240,2005
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, clarifications, typos fixed, references added
Scientific paper
10.1016/j.nuclphysb.2004.11.053
Linde has recently argued that compact flat or negatively curved spatial sections should, in many circumstances, be considered typical in Inflationary cosmologies. We suggest that the "large brane instability" of Seiberg and Witten eliminates the negative candidates in the context of string theory. That leaves the flat, compact, three-dimensional manifolds -- Conway's *platycosms*. We show that deep theorems of Schoen, Yau, Gromov and Lawson imply that, even in this case, Seiberg-Witten instability can be avoided only with difficulty. Using a specific cosmological model of the Maldacena-Maoz type, we explain how to do this, and we also show how the list of platycosmic candidates can be reduced to three. This leads to an extension of the basic idea: the conformal compactification of the entire Euclidean spacetime also has the topology of a flat, compact, four-dimensional space.
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