A Diagrammatic Approach to Scalar Field Correlators during Inflation

TL;DR

This work develops a diagrammatic, in-in (CTP) framework to address infrared divergences for a self-interacting scalar in de Sitter space, focusing on a quartic interaction and its large-$N$ extension. By deriving the Feynman rules in the Schwinger-Keldysh formalism and analyzing IR-dominated correlators, the authors identify and resum a class of diagrams (tadpole chains and towers) that generate nonperturbative IR effects, yielding a blue-tilted spectrum and a finite, mass-like IR regulator $m_{ m np}^2$ in the large-$N$ limit. In the $O(N)$-symmetric, large-$N$ regime, the trispectrum is shown to be enhanced by a factor of order $1/ oot 2 times olimits{ ext{λ}}$ relative to tree level, matching results obtained via stochastic methods and confirming the IR-resummation picture from a purely diagrammatic perspective. Overall, the paper demonstrates that IR IR divergences during inflation can be systematically resummed within the in-in formalism, providing a complementary viewpoint to stochastic approaches and highlighting the significance of non-Gaussian signals in the trispectrum for inflationary phenomenology.

Abstract

We consider a self-interacting scalar field in a de Sitter background and deal with the associated infrared divergences in a purely diagrammatic way using the in-in formalism. In the particular case of a large N O(N) invariant scalar field theory with quartic self-interactions we recover the result that the connected four-point correlation function, which is a signal of non-Gaussianity, is non-perturbatively enhanced with respect to its tree-level value.

Figures (10)

• Figure 1: An example of Keldysh Contour $\mathcal{C}$
• Figure 2: The loop is formed by a retarded propagator $G_R$ starting and ending at time $\tau_3$. It is identically zero.
• Figure 3: One tadpole $G_C$ and $G_R$ propagators
• Figure 4: Two-tadpole $G_C$ and $G_R$ propagators.
• Figure 5: Second order tower diagrams for $G_C$( left) and $G_R$( right).