Topology of Future Infinity in dS/CFT

TL;DR

This paper investigates how the topology of the universe at future infinity influences the Wheeler-de Witt wave function in dS/CFT, revealing rapid growth with topological complexity due to the Chern-Simons states.

Contribution

It computes the wave function's topology dependence in dS/CFT using Vasiliev and Einstein gravity, highlighting the growth and challenges in controlling it.

Findings

Wave function grows rapidly with topological complexity.

Chern-Simons states contribute to the growth.

Different contours in Einstein gravity yield similar topology dependence.

Abstract

The dS/CFT proposal of Anninos, Hartman, and Strominger relates quantum Vasiliev gravity in dS_4 to a large N vector theory in three dimensions. We use this proposal to compute the Wheeler-de Witt wave function of a universe having a particular topology at future infinity. This amplitude is found to grow rapidly with the topological complexity of the spatial slice; this is due to the plethora of states of the Chern-Simons theory that is needed to impose the singlet constraint. Various mechanisms are considered which might ameliorate this growth, but none seems completely satisfactory. We also study the topology dependence in Einstein gravity by computing the action of complex instantons; the wave function then depends on a choice of contour through the space of metrics. The most natural contour prescription leads to a growth with genus similar to the one found in Vasiliev theory, albeit with a different power of Newton's constant.