The IR stability of de Sitter QFT: Physical initial conditions

TL;DR

This paper demonstrates that in de Sitter space, correlators from physically motivated initial conditions approach the Hartle-Hawking state at late times, supporting the stability of the de Sitter quantum field theory.

Contribution

It shows that physically motivated initial conditions lead to late-time correlators matching the Hartle-Hawking state, extending quantum no-hair theorems with explicit Lorentz-signature analysis.

Findings

Correlators approach Hartle-Hawking state at late times

Physically motivated initial conditions lie in the dense set of states

Provides explicit renormalization techniques in Lorentz-signature

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 i) indicates that physically motivated initial conditions lie in this dense set, ii) provides a Lorentz-signature counter-part to the Euclidean techniques used to prove such theorems, and iii) provides an explicit example of the relevant renormalization techniques.