Complex geodesics in de Sitter space

Understand

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.