Quantum field thermalization in expanding backgrounds

Abstract

The 2PI effective action formalism for quantum fields out of equilibrium is set up in an expanding (Friedmann-Robertson-Walker) background. We write down and solve the evolution equations for a ϕ 4 model at O(λ 2 ) in a coupling expansion. We comment on issues of renormalization, lattice discretization and the range of applicability of the approach. A number of example calculations are presented, including thermalization and (p)reheating. Generalizations to more complicated systems and applications are discussed.

Quantum corrections to scalar field dynamics in a slow-roll space-time

“…These are typically based on a gradient expansion around the Minkowski vacuum, either through adiabatic regularisation [12][13][14][15][16] or at the level of the action using the Schwinger-deWitt expansion [17][18][19][20] for the 1PI effective action. In contrast to the 1PI expansion, in the 2-particle-irreducible (2PI) expansion one uses the dressed propagator in the Feynman diagrams.…”

“…6 We note that although we consider an out-of-equilibrium setup, as long as we compute the local correlator, truncating at one loop, we do not need to worry about the Schwinger-Keldysh contour, and distinguishing between field variables living on the upper and lower branch. Our G(x, x) is G ++ (x, x) in the notation of [21], and the statistical propagator F (x, x) in the notation of [16] and related. 7 To leading order our δ is proportional, but not identical, to the second potential slow-roll parameter…”

“…(4.18)-(4.19) below. 16 16 More precisely, the error of an iterative solution ǫi to equation (4.5), written as ǫ = f (ǫ), can be estimated by |ǫ − ǫ1| ≤ |f ′ (ǫ0)||ǫ1 − ǫ0|, assuming |f ′ (ǫ0)| ≪ 1, where ǫ0, ǫ1 and ǫ correspond to the zeroth iteration (classical solution), first iteration (classical + leading quantum correction) and the true solution, respectively. By direct computation we now find that the the size of the derivative f ′ (ǫ0) is roughly controlled by the dimensionless factors in eqs.…”

Nonperturbative resummation of de Sitter infrared logarithms in the large-Nlimit

“…in terms of the conformal time η and comoving spatial coordinates X, with a(η) = −1/η = e t with t ∈ R. Like general nonequilibrium quantum systems [26,[49][50][51][52], quantum field theories in cosmological spaces can be conveniently formulated using a closed contour C in the time coordinate [39,53,54]. The appropriate contour for conformal time is depicted in Fig.…”

Towards thermalization in heavy-ion collisions: CGC meets the 2PI formalism

“…When applied to the real-time evolution of nonequilibrium systems, the 2PI formalism can be naturally viewed as the field-theoretic generalization [13] of the classic, self-consistent ('Φ-derivable') method in quantum statistical mechanics [14,15]. A variety of nonequilibrium processes have been studied in this framework mostly in the context of scalar field theories [16,17,18,19,20,21,22,23]. In particular, it has been demonstrated that, starting from an arbitrary initial condition far from equilibrium, the 2PI dynamics drives the system towards the quantum equilibrium characterized by the Bose-Einstein distribution.…”