Lecture notes on interacting quantum fields in de Sitter space

TL;DR

<3-5 sentence high-level summary>This work investigates how non-conformal quantum fields in de Sitter space exhibit strong infrared corrections that survive beyond tree level, potentially challenging the stability of de Sitter space. By employing the Schwinger-Keldysh formalism, BD and alpha vacua analyses, and Dyson-Schwinger equations, the authors show that de Sitter invariance in loops is generally preserved only for the BD state in the expanding patch, while other vacua introduce IR-induced symmetry breaking and backreaction effects. They derive a kinetic equation for the IR-dominated Keldysh propagator, interpret the leading IR dynamics in terms of particle production and decay, and explore stationary versus explosive solutions, highlighting potential instability of dS space under nonsymmetric perturbations. The results illuminate the interplay between infrared dynamics, vacuum choice, and backreaction, with implications for quantum field theory in curved spacetime and cosmology."

Abstract

We discuss peculiarities of quantum fields in de Sitter space on the example of the self-interacting massive real scalar, minimally coupled to the gravity background. Non-conformal quantum field theories in de Sitter space show very special infrared behavior, which is not shared by quantum fields neither in flat nor in anti-de-Sitter space: in de Sitter space loops are not suppressed in comparison with tree level contributions because there are strong infrared corrections. That is true even for massive fields. Our main concern is the interrelation between these infrared effects, the invariance of the quantum field theory under the de Sitter isometry and the (in)stability of de Sitter invariant states (and of dS space itself) under nonsymmetric perturbations.

Figures (8)

• Figure 1: Each constant $X_0$ slice of this two-dimensional dS space is a circle of radius $(H^{-2} + X_0^2)$.
• Figure 2: The standard quadratic Penrose diagram of $D$-dimensional dS space, when $D > 2$. The straight thin line is the constant $t$ and/or $\theta$ slice.
• Figure 3: The rectangular Penrose diagram of the two-dimensional dS space. Note that the left and right sides of this rectangle are glued to each other. Thus, while on fig. \ref{['fig2']} the positions $\theta_1 = \pm \frac{\pi}{2}$ sit at the opposite poles of the spherical time slices, on the present figure the positions $\theta_1 = \pm \pi$ coincide.
• Figure 4: The boundary between the EPP and CPP is light-like and is situated at $\eta_\pm = + \infty$. We also show here the constant conformal time slices.
• Figure 5: While the solid line corresponds to $\phi_{cl}$, the dashed one --- to $\phi_q$.