The Size of Local Bispectrum and Trispectrum in a Non-Minimal Inflation

TL;DR

This paper investigates the size of local non-Gaussianities, specifically the bispectrum and trispectrum, during non-minimal slow-roll inflation using the $ ext{δ}N$ formalism, and compares results in different frames.

Contribution

It provides analytical expressions for non-Gaussianity parameters in non-minimal inflation and tests the model against Planck2015 data, extending analysis to Einstein frame.

Findings

Non-Gaussianity parameters are small but consistent with observations.

The model constraints are derived from Planck2015 data.

Comparison of results in Jordan and Einstein frames.

Abstract

Focusing on the local type primordial non-Gaussianities, we study the bispectrum and trispectrum during a non-minimal slow-roll inflation. We use the so-called $\delta N$ formalism to investigate the super-horizon evolution of the primordial perturbations in this setup. Firstly we obtain the main equations of the model and introduce the framework of the $\delta N$ formalism for this case. Then we give analytical expressions for the nonlinear parameters describing the non-Gaussianity in the slow-roll approximation. We analyze the bispectrum by its non-linear parameter, $f_{NL}$. Furthermore, we calculate $\tau_{NL}$ and $g_{NL}$ which are non-linear parameters characterizing the amplitude of trispectrum. Finally, by adopting a quadratic form for both the potential and non-minimal coupling (NMC) function, we test our setup in the light of Planck2015 data and constrain the model parameters space. Although the non-Gaussianity parameters are so small in this setup, this model is consistent with recent observation. We extend our analysis to see the situation in the Einstein frame and compare the results in these two frames.