Primordial non-Gaussianity in Horndeski-type model for Inflation

TL;DR

This paper analyzes the non-Gaussianity and power spectrum in a Horndeski scalar-tensor inflation model using quantum field theory methods, providing new calculations and reviewing existing literature.

Contribution

It introduces new techniques for calculating non-Gaussianity in Horndeski models and compares different formalisms for inflationary perturbations.

Findings

Calculated the power spectrum and bispectrum in the Horndeski model.

Derived the $f_{NL}$ parameter and spectral index for the model.

Provided a comprehensive review of inflationary non-Gaussianity literature.

Abstract

We consider a member of the family of scalar-tensor theories of Inflation - the so-called Horndeski model for Inflation, for which we calculate the non-Gaussianity (NG) and the power spectrum of curvature perturbations. We concentrate on the determination of the power spectrum, and the bi-spectrum along with the associated $f_\mathrm{NL}$ parameter and the Spectral Index. We follow the methodology outlined within the Quantum field theory framework (S-matrix approach and Weinberg's 'in-in' formalism) and compare - whenever necessary - our findings with those obtained via the traditional $\delta$N formalism. The work contained herein is an extensive review of the existing literature on this subject and the 'Inflationary theory' in general, along with some newly developed techniques and calculations.