  The two-point function of a free massive scalar field on a fixed background
can be evaluated in the large mass limit by using a semiclassical geodesic
approximation. In de Sitter space, however, this poses a puzzle. Certain
spacelike separated points are not connected by real geodesics despite the
corresponding two-point function in the Bunch-Davies state being non-vanishing.
We resolve this puzzle by considering complex geodesics after analytically
continuing to the sphere. We compute one-loop corrections to the correlator and
discuss the implications of our results to de Sitter holography.
