Observational Signatures and Non-Gaussianities of General Single Field Inflation

TL;DR

Chen et al. provide a comprehensive, model-independent analysis of primordial scalar non-Gaussianities in single-field inflation with a general Lagrangian P(X, φ) and arbitrary sound speed. They show that, to first order in slow variation, the bispectrum is fully specified by five parameters (c_s, λ/Σ, ε, η, s) and identify several distinct shapes that emerge in different sectors of parameter space, especially for c_s ≪ 1. The paper applies the general result to slow-roll, DBI, and K-inflation, discusses running and vacuum-state effects, and outlines how non-Gaussian signatures can serve as powerful probes of the inflationary dynamics and possible UV completions. This work provides a practical framework for interpreting upcoming CMB and large-scale-structure measurements of non-Gaussianity.

Abstract

We perform a general study of primordial scalar non-Gaussianities in single field inflationary models in Einstein gravity. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ``shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results.

Figures (5)

• Figure 1: The shape of $-{\cal A}_\lambda/k_1k_2k_3$
• Figure 2: The shape of ${\cal A}_c/k_1k_2k_3$
• Figure 3: The shape of $-{\cal A}_\epsilon/k_1k_2k_3$
• Figure 4: The shape of $|\tilde{{\cal A}}_\lambda|/k_1k_2k_3$
• Figure 5: The shape of $|\tilde{{\cal A}}_c|/k_1k_2k_3$