Late-Time Correlators and Complex Geodesics in de Sitter Space

• Main Authors: Aalsma, Lars, Faruk, Mir Mehedi, van der Schaar, Jan Pieter, Visser, Manus, de Witte, Job
• Format: Journal Article
• Language: English
• Published: 16-08-2023
• Subjects: Physics - High Energy Physics - Theory
• DOI: 10.48550/arxiv.2212.01394

SciPost Phys. 15, 031 (2023) 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.