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