On Cosmological Singularities in String Theory

TL;DR

This paper investigates the evolution of a 3+1 dimensional universe with a three-sphere topology under small perturbations, analyzing singularities and their potential resolution within string theory.

Contribution

It explores how specific worldsheet deformations lead to cosmological singularities and discusses the possibility of string theory resolving these singularities.

Findings

Small deformations cause big-bang and big-crunch singularities.

The radius of the three-sphere can diverge at finite time without collapsing.

String theory likely resolves certain cosmological singularities.

Abstract

We study the time evolution of a $3+1$ dimensional spacetime, where space is a large three-sphere, due to small perturbations of the background fields. We focus on two classes of deformations. One corresponds on the worldsheet to time-dependent non-abelian Thirring deformations. The other to perturbations of the radius of the three-sphere. In the former case, we find that small deformations generically lead to big-bang and big-crunch singularities, near which the spacetime becomes highly anisotropic. We argue that string theory likely resolves these singularities. In the latter case, general solutions have the property that the radius of the three-sphere goes to infinity at a finite time, but there are no solutions in which it collapses to zero. We also discuss the interplay of these spacetime properties with the corresponding worldsheet RG flows.