On the IR Divergences in de Sitter Space: loops, resummation and the semi-classical wavefunction

Abstract

In this paper, we revisit the infrared (IR) divergences in de Sitter (dS) space using the wavefunction method, and explicitly explore how the resummation of higher-order loops leads to the stochastic formalism. In light of recent developments of the cosmological bootstrap, we track the behaviour of these nontrivial IR effects from perturbation theory to the non-perturbative regime. Specifically, we first examine the perturbative computation of wavefunction coefficients, and show that there is a clear distinction between classical components from tree-level diagrams and quantum ones from loop processes. Cosmological correlators at loop level receive contributions from tree-level wavefunction coefficients, which we dub classical loops. This distinction significantly simplifies the analysis of loop-level IR divergences, as we find the leading contributions always come from these classical loops. Then we compare with correlators from the perturbative stochastic computation, and find the results there are essentially the ones from classical loops, while quantum loops are only present as subleading corrections. This demonstrates that the leading IR effects are contained in the semi-classical wavefunction which is a resummation of all the tree-level diagrams. With this insight, we go beyond perturbation theory and present a new derivation of the stochastic formalism using the saddle-point approximation. We show that the Fokker-Planck equation follows as a consequence of two effects: the drift from the Schrödinger equation that describes the bulk time evolution, and the diffusion from the Polchinski's equation which corresponds to the exact renormalization group flow of the coarse-grained theory on the boundary. Our analysis highlights the precise and simple link between the stochastic formalism and the semi-classical wavefunction.

59 pages, 5 figures; v2: published version with minor revisions and references added

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• Regularizing infrared divergences in de Sitter spacetime: Loops, dimensional regularization, and cutoffs
• Perturbative unitarity bounds from momentum-space entanglement
• The Massive Flat Space Limit of Cosmological Correlators
• IR finite correlation functions in de Sitter space, a smooth massless limit, and an autonomous equation
• The Asymptotic Structure of Cosmological Integrals
• Bananas are Unparticles: Differential Equations and Cosmological Bootstrap
• Resummation of local and non-local scalar self energies via the Schwinger-Dyson equation in de Sitter spacetime
• Cosmological Infrared Subtractions & Infrared-Safe Computables
• Boundary choices and one-loop complex gravitational path integral
• Cosmological Non-Gaussianity from Neutrino Seesaw Mechanism
• RG flows in de Sitter: c-functions and sum rules
• From the Fokker-Planck equation to perturbative QFT's results in de Sitter space
• A Match Made in Heaven: Linking Observables in Inflationary Cosmology
• Perturbative unitarity bounds on field-space curvature in de Sitter spacetime: purity vs scattering amplitude
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