Complex geodesics in de Sitter space

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.

Automated summary

The two-point function of a free massive scalar field on a fixed background can be evaluated using a semiclassical geodesic approximation. However, in de Sitter space, there is a puzzle where certain spacelike separated points are not connected by real geodesics, despite the non-vanishing two-point function in the Bunch-Davies state. This puzzle is resolved by considering complex geodesics after analytically continuing to the sphere. One-loop corrections to the correlator are computed, and the implications of the results for de Sitter holography are discussed.