Lars Aalsma, Mir Mehedi Faruk, Jan Pieter van der Schaar, Manus Visser, Job de Witte
SciPost Phys. 15, 031 (2023) ·
published 26 July 2023
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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.
Edward K. Morvan, Jan Pieter van der Schaar, Manus R. Visser
SciPost Phys. 14, 022 (2023) ·
published 23 February 2023
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We compute the on-shell Euclidean action of Schwarzschild-de Sitter black holes, and take their contributions in the gravitational path integral into account using the formalism of constrained instantons. Although Euclidean de Sitter black hole geometries have conical singularities for generic masses, their on-shell action is finite and is shown to be independent of the Euclidean time periodicity and equal to minus the sum of the black hole and cosmological horizon entropy. We apply this result to compute the probability for a nonrotating, neutral arbitrary mass black hole to nucleate spontaneously in empty de Sitter space, which separates into a constant and a "non-perturbative" contribution, the latter corresponding to the proper saddle-point instanton in the Nariai limit. We also speculate on some further applications of our results, most notably as potential non-perturbative corrections to correlators in the de Sitter vacuum.
Dr van der Schaar: "We thank the referee for the c..."
in Submissions | report on On the Euclidean Action of de Sitter Black Holes and Constrained Instantons