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The IR stability of de Sitter QFT: physical initial conditions

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Abstract

This work uses Lorentz-signature in-in perturbation theory to analyze the late-time behavior of correlators in time-dependent interacting massive scalar field theory in de Sitter space. We study a scenario recently considered by Krotov and Polyakov in which the coupling g turns on smoothly at finite time, starting from g = 0 in the far past where the state is taken to be the (free) Bunch–Davies vacuum. Our main result is that the resulting correlators (which we compute at the one-loop level) approach those of the interacting Hartle–Hawking state at late times. We argue that similar results should hold for other physically-motivated choices of initial conditions. This behavior is to be expected from recent quantum “no hair” theorems for interacting massive scalar field theory in de Sitter space which established similar results to all orders in perturbation theory for a dense set of states in the Hilbert space. Our current work (1) indicates that physically motivated initial conditions lie in this dense set, (2) provides a Lorentz-signature counter-part to the Euclidean techniques used to prove such theorems, and (3) provides an explicit example of the relevant renormalization techniques.

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Authors and Affiliations

  1. Department of Physics, University of California, Santa Barbara, CA, 93016, USA

    Donald Marolf & Ian A. Morrison

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  1. Donald Marolf
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  2. Ian A. Morrison
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Correspondence to Donald Marolf.

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This article is dedicated to Joshua Goldberg, with whom one of the authors (DM) enjoyed discussing all manner of gravitational physics during his time at Syracuse University. The article reflects Josh’s continued emphasis on understanding not only the mathematics of a given problem, but also the physics, and in particular in verifying that a given mathematical theorem is indeed relevant to the physical problem at hand.

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Marolf, D., Morrison, I.A. The IR stability of de Sitter QFT: physical initial conditions. Gen Relativ Gravit 43, 3497–3530 (2011). https://doi.org/10.1007/s10714-011-1233-3

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