Complex Geodesics in the Nariai Geometry

TL;DR

This paper analyzes two-point correlation functions of heavy scalar fields in the Nariai geometry using heat kernel formalism and complex geodesics, highlighting the importance of phase considerations to avoid singularities.

Contribution

It extends previous de Sitter space results by incorporating complex geodesics and phase analysis in the Nariai geometry for scalar field correlations.

Findings

Derived correlation functions via geodesic approximation.

Identified the role of complex geodesics and phase in correlator behavior.

Extended de Sitter results to Nariai geometry.

Abstract

We study two-point correlation functions of heavy scalar fields in the Nariai geometry. Utilizing the heat kernel formalism, we obtain this result from a geodesic approximation to the two-point function on a product of spheres. By analytically continuing one of the spheres, we obtain the correlation function in the Nariai geometry. This result involves a sum over complex geodesics, extending previous results in pure de Sitter space. We emphasize the important role of the phase of each geodesic contribution, which needs to be taken into account to avoid spurious singularities in the correlator.