Analytical Study for Primordial Non-Gaussianity in the gravity 4D Einstein-scalar-Gauss-Bonnet Inflation

TL;DR

This paper analyzes the non-Gaussian features of a 4D Einstein-scalar-Gauss-Bonnet inflation model using Planck data, employing the in-in formalism to constrain non-Gaussianity parameters and confirm the model's slow-roll behavior.

Contribution

It provides a novel analysis of non-Gaussianity in the 4D Einstein-Gauss-Bonnet inflation model using third-order perturbation and Planck data constraints.

Findings

The model exhibits slow-roll behavior in the squeezed limit.

Non-Gaussianity is consistent with single scalar field inflation.

Gauss-Bonnet term is topologically invariant in D<5 spacetimes.

Abstract

An inflationary model can be constrained by non-gaussian statistics as a parameter in the LSS (Large Scale Structure) distribution, and in the radiation of CMB (Cosmic Microwave Background) fluctuating temperature. Data on the CMB from Planck Collaboration provide up-to-date constraints on the parameters controlling the degree of non-Gaussianity in certain inflationary models, thus supporting or not supporting the model. Setting the non-Gaussianity parameter investigated in this study can be a reference whether or not it is a good parameter in constraining cosmological inflation models. This study attempts to examine the non-Gaussianity of the 3+1-dimensional 4DEGB gravitational cosmological inflation model starting from random field statistics. The non-Gaussian signature generated by the model is quantified, and the parameters controlling the degree of non-Gaussianity are constrained using data observation of Planck Collaboration. The method used in investigating non-Gaussianity is the in-in formalism, applied after obtaining the 3-point of $\zeta$ (curvature perturbation) terms of the perturbation expansion to the third order. The 3-point correlation function helps to create a bispectrum used to investigate the non-gaussinity of the inflation model. The results of this study show that the model tested is the slow roll pressed in the squeezed limit, because it witnesses a dominant local shape function. It has such as the non-gaussianity possessed by the single scalar field inflation as confirmation that Gauss-Bonnet term within Einstein-Hilbert action is topologically invariant in $D<5$ spacetimes.