On Cosmological Singularities in String Theory

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.