Curvaton with Nonminimal Derivative Coupling to Gravity II: Full Perturbation Analysis

TL;DR

This paper thoroughly analyzes the perturbations of a curvaton model with nonminimal derivative coupling to gravity, including up to third-order correlations, revealing non-Gaussian features consistent with PLANCK data and predicting observable signatures.

Contribution

It provides the first full third-order perturbation analysis of the nonminimal derivative coupled curvaton model, including scalar, tensor, and mixed non-Gaussianities.

Findings

3-point functions fit PLANCK non-Gaussianity data

Shape functions peak at squeezed and equilateral limits

Predictions for future observational tests

Abstract

In our previous work \cite{Feng:2013pba}, we have shown a curvaton model where the curvaton has a nonminimal derivative coupling to gravity. Such a coupling could bring us scale-invariance of the perturbations for wide range constant values of the equation-of-state of the cosmic background at the early time. In this paper, we continue our study by fully analyzing its perturbations up to the third order. Apart from the usual 2-point correlation function that has already been calculated in \cite{Feng:2013pba}, we have also taken into account the 3-point correlation functions including pure scalar part, pure tensor part, as well as the cross-correlations between scalar and tensor perturbation modes. We find that for pure scalar part, the 3-point correlation functions can generate non-Gaussianities that fits the PLANCK data very well. For pure tensor and mixed parts, the shape functions have peaks at squeezed and equilateral limits respectively, responsible for sizable $f_{NL}^{sqz}$ and $f_{NL}^{eql}$, which could be tested by the future observatioanl data.