On Soft Limits of Inflationary Correlation Functions

TL;DR

The paper develops a universal framework for soft limits in inflationary correlators, clarifying how collapsed (soft internal) and squeezed (soft external) limits constrain the spectrum of light fields during inflation. It derives and interprets key bounds and consistency relations, showing how single-source versus multi-source scenarios affect the soft behavior and offering a precise interpretation of additional states beyond the inflaton. The QSFI case study provides explicit in-in calculations, revealing mass-dependent scaling in squeezed limits and a boosted collapsed trispectrum, linking microscopic couplings to observable signatures. This work strengthens the idea of using non-Gaussianity as a particle detector for early-universe physics and outlines observational paths for future probes of the inflationary field content.

Abstract

Soft limits of inflationary correlation functions are both observationally relevant and theoretically robust. Various theorems can be proven about them that are insensitive to detailed model-building assumptions. In this paper, we re-derive several of these theorems in a universal way. Our method makes manifest why soft limits are such an interesting probe of the spectrum of additional light fields during inflation. We illustrate these abstract results with a detailed case study of the soft limits of quasi-single-field inflation.

Figures (5)

• Figure 3: Conformal diagram of de Sitter space. The inflationary background picks out a preferred time-slicing.
• Figure 4: Particle spectrum of quasi-single-field inflation.
• Figure 5: Perturbative description of $N$-point functions in quasi-single-field inflation.
• Figure 6: Particle spectra of inflationary models and their observational signatures.
• Figure 7: Illustration of the contour employed in the computation of $in$-$in$ correlation functions.