Late-Time Correlators and Complex Geodesics in de Sitter Space
arXiv:2212.01394 · doi:10.21468/SciPostPhys.15.1.031
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.
arXiv comment18 pages, 8 figures. v2: 19 pages + 2 pages appendices, 11 figures. Matches published version
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