Large Non-Gaussianity Implication for Curvaton Scenario

TL;DR

This work investigates the curvaton scenario as a source of local-type primordial non-Gaussianity and derives a parameter bound linking non-Gaussianity to the inflationary scale. By arguing that the typical curvaton energy density during inflation is bounded below by $H_*^4$ through gradient energy and de Sitter fluctuations, it establishes an upper limit $f_{NL} \lesssim 518 \cdot r^{1/4}$, with current data giving $f_{NL} < 346$ for $r<0.20$. The analysis also connects the spectral index through $n_s-1 = 2\eta_{\sigma\sigma} - 2\epsilon_H$ and discusses the challenges of achieving a red tilt within the curvaton framework, noting that multi-field or chain-inflation scenarios may accommodate the observed tilt. The results imply that a large local non-Gaussianity would point to high-scale inflation (near the GUT scale) and provide a discriminant from Ekpyrotic models via gravitational-wave signatures, making $f_{NL}$ a crucial probe of early-Universe physics and string-theory-inspired scenarios.

Abstract

We argue that the typical energy density of a light scalar field should not be less than $H^4$ in the inflationary Universe. This requirement implies that the non-Gaussianity parameter $f_{NL}$ is typically bounded by the tensor-scalar ratio $r$ from above, namely $f_{NL}\lesssim 518\cdot r^{1\over 4}$. If $f_{NL}=10^2$, inflation occurred around the GUT scale.

Figures (1)

• Figure 1: Evolution of the perturbation mode and the Hubble radius.