Late-Time Correlators and Complex Geodesics in de Sitter Space

TL;DR

This paper derives a geodesic approximation for two-point correlators of a massive scalar in de Sitter space at late times, revealing exponential decay linked to complex geodesics and discussing implications for de Sitter entropy.

Contribution

It introduces a novel geodesic approximation involving complex conjugate geodesics for late-time correlators in de Sitter space, connecting geometric and quantum properties.

Findings

The correlator decays exponentially at late times.

The approximation involves a sum over complex conjugate geodesics.

The decay behavior challenges the finite entropy of de Sitter space.

Abstract

We study two-point correlation functions of a massive free scalar field in de Sitter space using the heat kernel formalism. Focusing on two operators in conjugate static patches we derive a geodesic approximation to the two-point correlator valid for large mass and at late times. This expression involves a sum over two complex conjugate geodesics that correctly reproduces the large-mass, late-time limit of the exact two-point function in the Bunch-Davies vacuum. The exponential decay of the late-time correlator is associated to the timelike part of the complex geodesics. We emphasize that the late-time exponential decay is in tension with the finite maximal entropy of empty de Sitter space, and we briefly discuss how non-perturbative corrections might resolve this paradox.