More on the Non-Gaussianity of Perturbations in a Nonminimal Inflationary Model

R Shojaee,F Darabi,K Nozari

doi:10.1155/2018/2343896

Abstract

We study nonlinear cosmological perturbations and their possible non-Gaussian character in an extended nonminimal inflation where gravity is coupled nonminimally to both the scalar field and its derivatives. By expansion of the action up to the third order, we focus on the nonlinearity and non-Gaussianity of perturbations in comparison with recent observational data. By adopting an inflation potential of the form V(ϕ)=1/nλϕn, we show that, for n=4, for instance, this extended model is consistent with observation if 0.013<λ<0.095 in appropriate units. By restricting the equilateral amplitude of non-Gaussianity to the observationally viable values, the coupling parameter λ is constrained to the values λ<0.1.

Highlights

The idea of cosmological inflation is capable of addressing some problems of the standard big bang theory, such as the horizon, flatness, and monopole problems
It can provide a reliable mechanism for generation of density perturbations responsible for structure formation and temperature anisotropies in Cosmic Microwave Background (CMB) spectrum [1,2,3,4,5,6,7,8]
It has been shown that a model with nonminimal coupling between the kinetic terms of the inflaton and the Einstein tensor preserves the unitary bound during inflation [34]

Summary

Introduction

The idea of cosmological inflation is capable of addressing some problems of the standard big bang theory, such as the horizon, flatness, and monopole problems. Planck team have obtained some constraints on the primordial nonGaussianity [12,13,14] It seems that extended models of inflation which can explain or address this scaledependence and non-Gaussianity of perturbations are more desirable. In this paper we extend the nonminimal inflation models to the case that a canonical inflaton field is coupled nonminimally to the Advances in High Energy Physics gravitational sector and in the same time the derivatives of the field are coupled to the background geometry (Einstein’s tensor). This model provides a more realistic framework for treating cosmological inflation in essence. We are able to constrain parameter space of the model in comparison with observation

Field Equations

Second-Order Action

Third-Order Action

Confronting with Observation

Summary and Conclusion