$λφ^4$ in dS

TL;DR

This work tackles infrared divergences of light scalars in de Sitter space by formulating a rigorous nonperturbative framework for long-wavelength modes. By splitting modes into short (perturbative) and long (ultra-local, semiclassical) sectors and deriving a Fokker-Planck–like evolution for long modes, the authors establish a BD vacuum attractor, de Sitter invariance, and thermality in the static patch. They develop an EFT for long modes, compute leading and subleading correlators for $\lambda\phi^4$, and extend the analysis to large-$N$, providing a controlled, systematic expansion in $\sqrt{\lambda}$ and auxiliary parameters. The results show non-Gaussian, equilibrium long-mode distributions and demonstrate perturbative control over IR effects, with clear pathways to including gradient and quantum corrections.

Abstract

We resolve the issue of infrared divergences present in theories of light scalar fields on de Sitter space.

Figures (12)

• Figure 1: One-loop ( left) and two-loop ( right) diagrams for the two-point function of $\phi$. Lines with crosses represent correlation functions, without crosses represent Green's functions.
• Figure 2: Tree-level Witten diagram contributing to the $\lambda\phi^4$ term in the exponent of the wave function.
• Figure 3: Generic Witten diagram contributing to the wave function.
• Figure 4: Pictorial representation of the window function that splits the long and the short modes.
• Figure 5: Pictorial representation to the two contributions to the long-wavelength dynamics. The diffusion due to the short modes becoming long, and the drift from the evolution of the long modes. It is expected that an equilibrium value with the typical values, for $V=\lambda\phi^4$, of order $\phi\sim H/\lambda^{1/4}$ is reached. We will make this picture rigorous.