Late-Time Correlators and Complex Geodesics in 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.

18 pages, 8 figures. v2: 19 pages + 2 pages appendices, 11 figures. Matches published version

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• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
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• Deriving the Gibbons-Maldacena-Nunez no-go theorem from the Raychaudhuri equation
• Quasinormal Modes and the Switchback Effect in Schwarzschild-de Sitter
• Accelerated paths and Unruh effect II: finite time detector response in (Anti) de Sitter spacetime and Huygen's Principle