Inflation, Large Branes, and the Shape of Space

TL;DR

This paper investigates the stability of flat and negatively curved spatial sections in inflationary cosmology within string theory, showing that only certain flat compact manifolds are viable, with implications for the topology of the universe.

Contribution

It demonstrates that the large brane instability rules out negatively curved spaces and narrows down the flat candidates to three specific platycosms, extending to four-dimensional topologies.

Findings

Negative curvature candidates are eliminated by string theory instabilities.

Only three flat, compact 3-manifolds remain viable as spatial sections.

The topology of the entire spacetime may also be constrained to flat, compact four-dimensional spaces.

Abstract

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.