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

TL;DR

This paper analyzes primordial non-Gaussianity in a four-dimensional Einstein–scalar–Gauss–Bonnet inflation model by computing the curvature perturbation bispectrum $B(k_1,k_2,k_3)$ with the in‑in formalism, deriving the second- and third-order actions for the curvature perturbation $\zeta$ and evaluating the tree-level non-Gaussian signal. The resulting shape is dominated by the local template in the squeezed limit $k_1\ll k_2\approx k_3$, yielding a bispectrum that can be written as $S(k_1,k_2,k_3) \approx 2(3\varepsilon-\eta) S^{local} + \frac{5}{3}\varepsilon S^{equil}$. The amplitude is slow-roll suppressed and lies outside current Planck bounds but remains within theoretical expectations, indicating consistency with single-field inflation aesthetics. A template-based comparison with other inflationary models shows the 4D ESGB predictions are closely aligned with Local-type NG, allowing Planck local-template constraints to provide meaningful tests of the model’s viability.

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 $ζ$ (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.