Topology of Future Infinity in dS/CFT

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.

1+32 pages

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• Towards a quantum theory of de Sitter space
• A Holographic Framework for Eternal Inflation
• Higher Spin de Sitter Holography from Functional Determinants

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• Spin Structures and Exact Dualities in Low Dimensions
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• Late-time Structure of the Bunch-Davies FRW Wavefunction
• Chern-Simons-Matter Theories at Large Baryon Number
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