Scale Dependent Local Non-Gaussianity from Loops

TL;DR

The paper addresses generating large, scale-dependent local-like non-Gaussianity in inflation without spoiling the power spectrum. It develops a minimal two-field hybrid inflation model where NG arises from loop (c-loop) corrections in the transfer of field fluctuations to curvature, analyzed via the $\delta N$ formalism. The results show $f_{NL}$ can reach ${\cal O}(100)$ with positive running $n_{NG}$ around $0.2$ on CMB scales and about $0.1$ on LSS scales, with the non-Gaussian signal growing toward smaller scales; the shape remains close to local and a running trispectrum $\tau_{NL}$ is predicted as well. These signals could be probed by Planck and large-scale structure surveys, and the work outlines several future directions for relaxing assumptions and exploring broader model spaces.

Abstract

We analyze multi-field inflationary systems which yield strongly scale dependent non-Gaussianity with a shape that is very close to the local shape. As in usual multi-field models, the non-Gaussianity arises from the non-linear transfer of scalar field fluctuations to curvature perturbations. Here we consider models in which higher order terms (loops) dominate over the lowest order source of non-linearity. The magnitude of non-Gaussianity depends on an infrared cutoff which is determined by our observational probes measuring non-Gaussianity. In our models, the running is positive and large (n_{NG} ~ 0.2) on CMB scales. The magnitude of the bispectrum is maximally of order O(100), and grows on small scales. This can lead to interesting signals for large scale structure.

Figures (3)

• Figure 1: This figure depicts the trajectory in field space. The blue (dashed) line denote the surface of reheating defined by $f(\phi_e,\chi_e)=0$ and it is assumed to be thin. The classical trajectory is in the $\phi$ direction (red/dotted line) but both $\delta\phi$ and $\delta\chi$ will induce curvature perturbations.
• Figure 2: The 1-loop diagram. In our case, each vertex is accompanied by a factor of $N'^3\gamma_{,\chi}^3$ while each internal propagator is given by $\frac{2\pi^2\mathcal{P}}{p^3}$. More detailed Feynman rules for use with the $\delta N$ expansion (which we are not carefully describing here) can be found in Byrnes:2007tm.
• Figure 3: Plot of the approximate shape $B(k_1,k_1x_2,k_1x_3) x_2^2 x_3^2 k_1^6$ (with $B(k_1,k_2,k_3)$ given by Eq. (5.6)) in terms of $x_2 = \frac{k_2}{k_1}$ and $x_3= \frac{k_3}{k_1}$ for $k_1 = 0.5$ (left) and $k_1 = 1.5$ (right). The shape was restricted to be in the quadrant defined by $k_1 (1-x_2) < k_1 x_3 < k_1 x_2$ due to momentum conservation and to avoid overcounting identical triangle configurations (see Babich:2004gb). The shape is clearly very close to local with the strongest signal in the squeezed limit when $k_3 = k_1 x_3 \rightarrow 0$. The overall magnitude of NG increases with the wavenumber $k_1$ or as we consider smaller wavelengths.