Towards a Big Crunch Dual

TL;DR

The paper shows that in low-energy string theory limits, smooth asymptotically AdS initial data can evolve to a big crunch, by constructing explicit ${\cal N}=8$, $D=4$ and related ${\cal N}=8$, $D=5$ supergravity setups with AdS-invariant boundary conditions labeled by a parameter $f$. It proves a general negative-energy consequence of scalar solitons, builds explicit solitons and instantons, and demonstrates that analytic continuation of these instantons leads to big crunch singularities, potentially visible to the dual CFT. The dual description involves triple-trace deformations that can destabilize the CFT at finite time, suggesting the big crunch could be an endpoint of evolution even in the full string theory. These results highlight how boundary conditions control stability and cosmic censorship in AdS/CFT-inspired cosmologies and motivate further study of the dual quantum descriptions.

Abstract

We show there exist smooth asymptotically anti-de Sitter initial data which evolve to a big crunch singularity in a low energy supergravity limit of string theory. This opens up the possibility of using the dual conformal field theory to obtain a fully quantum description of the cosmological singularity. A preliminary study of this dual theory suggests that the big crunch is an endpoint of evolution even in the full string theory. We also show that any theory with scalar solitons must have negative energy solutions. The results presented here clarify our earlier work on cosmic censorship violation in N=8 supergravity.

Figures (3)

• Figure 1: Soliton solution $\phi(r)$ with boundary conditions specified by $f=-1/4$.
• Figure 2: Instanton solution $\phi(\rho)$ with boundary condition $f=-1/4$.
• Figure 3: Instanton solution $\phi(\rho)$ with boundary condition $f=1$.