The IR stability of de Sitter QFT: Physical initial conditions

TL;DR

This work demonstrates, at one-loop order, that time-dependent couplings turning on in de Sitter space drive two-point functions toward those of the interacting Hartle-Hawking state, for a broad class of physically reasonable initial conditions. By working in Lorentzian in-in perturbation theory and employing Pauli–Villars regularization with Mellin–Barnes techniques, the authors show that boundary terms arising from the transition region decay at late times, leaving HH-like correlators. The results reinforce the quantum cosmic no-hair intuition and provide explicit, renormalized constructions that extend Euclidean insights to Lorentzian signature. The analysis suggests that the attractor behavior of HH correlators persists beyond naive vacua and may hold to all orders in perturbation theory for a dense set of initial states in de Sitter space.

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.

Figures (3)

• Figure 1: The Penrose diagram of de Sitter. We consider the state $\left| \Psi \right\rangle$ defined by the Bunch-Davies vacuum on a Cauchy surface $\Sigma$. The interaction turns on across the region $\mathcal{R}$ via a smooth coupling function $g(x)$ such that $g(x)=g_f$ in the causal future of $\mathcal{R}$ and $g(x)=0$ in the causal past of $\mathcal{R}$. We compute the time-ordered 2-point function $\left\langle T\phi(x_1)\phi(x_2) \right\rangle_\Psi$ of two points in the distant future.
• Figure 2: Corrections to the time-ordered 2-point function $\left\langle T \phi(x_1)\phi(x_2) \right\rangle_\Psi$ due to the interaction $-\frac{1}{2}g(x)\phi^2(x)$. The $O(g(x))$ correction is depicted in Fig. (a) while the $O(g^2(x))$ correction is depicted in Fig. (b). It is convenient for computation to label each leg of the diagram by a distinct mass parameter $\sigma_i$.
• Figure 3: The $O(g^2(x))$ correction to the time-ordered 2-point function $\left\langle T\phi(x_1)\phi(x_2) \right\rangle_\Psi$ in a theory with an $g(x)\phi^3(x)$ interaction. Once again we label each leg of the diagram by a distinct mass parameter $\sigma_i$.