Pre-Inflationary Spacetime in String Cosmology

TL;DR

This paper explores the stability of pre-inflationary spacetime in string cosmology, showing that maintaining stability imposes constraints on early universe geometry and may prevent cosmological singularities.

Contribution

It demonstrates that stability conditions in string cosmology restrict early universe geometries and proposes a candidate structure that could avoid singularities.

Findings

Toral spatial sections are marginally stable in string theory.

Stability conditions constrain early universe geometries.

A candidate structure preventing cosmological singularities is proposed.

Abstract

Seiberg and Witten have shown that the non-perturbative stability of string physics on conformally compactified spacetimes is related to the behaviour of the areas and volumes of certain branes as the brane is moved towards infinity. If, as is particularly natural in quantum cosmology, the spatial sections of an accelerating cosmological model are flat and compact, then the spacetime is on the brink of disaster: it turns out that the version of inflationary spacetime geometry with toral spatial sections is marginally stable in the Seiberg-Witten sense. The question is whether the system remains stable before and after Inflation, when the spacetime geometry is distorted away from the inflationary form but still has flat spatial sections. We show that it is indeed possible to avoid disaster, but that requiring stability at all times imposes non-trivial conditions on the spacetime geometry of the early Universe in string cosmology. This in turn allows us to suggest a candidate for the structure which, in the earliest Universe, forbids cosmological singularities.