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We study the partition function of the free Sp(N) conformal field theoryrecently conjectured to be dual to asymptotically de Sitter higher-spin gravityin four-dimensions. We compute the partition function of this CFT on a roundsphere as a function of a finite mass deformation, on a squashed sphere as afunction of the squashing parameter, and on an S2xS1 geometry as a function ofthe relative size of S2 and S1. We find that the partition function isdivergent at large negative mass in the first case, and for small $S^1$ in thethird case. It is globally peaked at zero squashing in the second case. Throughthe duality this partition function contains information about the wavefunction of the universe. We show that the divergence at small S1 occurs alsoin Einstein gravity if certain complex solutions are included, but thedivergence in the mass parameter is new. We suggest an interpretation for thisdivergence as indicating an instability of de Sitter space in higher spingravity, consistent with general arguments that de Sitter space cannot bestable in quantum gravity.

The Wave Function of Vasiliev's Universe - A Few Slices Thereof