Quantum Stability of a w < - 1 Phase of Cosmic Acceleration

TL;DR

This work analyzes the stability of a massless, minimally coupled scalar with a λ φ^4 interaction in a locally de Sitter (inflationary) background, where quantum effects can induce a transient super-acceleration. By deriving and solving the quantum-corrected effective mode equation at one- and two-loop order with Schwinger-Keldysh formalism, the authors show the mode amplitude decays in time, consistent with the development of a positive, non-tachyonic mass-squared and hence stability. The leading infrared behavior is cross-validated using Starobinsky’s stochastic inflation approach, with both methods yielding identical leading-log results up to λ^2 corrections. The findings indicate that, for λ ≪ 1, the instability is self-limiting and the system remains stable over a long, but finite, inflationary period, with quantum and stochastic analyses in agreement. This has implications for understanding quantum backreaction and the viability of transient w < -1 phases in cosmology.

Abstract

We consider a massless, minimally coupled scalar with a quartic self-interaction which is released in Bunch-Davies vacuum in locally de Sitter background of an inflating universe. It was shown, in this system, that quantum effects can induce a temporary phase of super-acceleration causing a violation of the Weak Energy Condition on cosmological scales. In this paper we investigate the system's stability by studying the behavior of linearized perturbations in the quantum-corrected effective field equation at one and two-loop order. We show that the time dependence we infer from the quantum-corrected mode function is in perfect agreement with the system developing a positive mass squared. The maximum induced mass remains perturbatively small and it does not go tachyonic. Thus, the system is stable.

Figures (2)

• Figure 1: Generic one-loop diagram with mass counterterm
• Figure 2: Generic snowman diagram with mass counterterm.