Schwinger\u2013Keldysh mechanism in extended quasi-single field inflation

Haidar Sheikhahmadi

doi:10.1140/epjc/s10052-019-6969-z

Abstract

We study an extension of quasi-single field model of inflation containing multiple semi-heavy isocurvaton fields using the Schwinger–Keldysh mechanism. We calculate the amplitudes and the shapes of the bispectrum and the trispectrum. We show that the diagrammatic approach associated with the Schwinger–Keldysh mechanism simplifies the analysis considerably compared to standard in-in formalism. This method is helpful to study the spectroscopy of masses and couplings of light and semi-heavy fields during inflation.

Highlights

Investigating bispectrum, especially trispectrum based on in-in formulation is conducted comprehensively in recent works and articles about single-field models. Following this model, author in [52] has conducted multifield that contains abstruse mathematics. Besides this conventional calculating methods, reference author’s [78] used diagrammatic method and some methods based on Schwinger–Keldysh (SK) formalism [87,88,89] which greatly reduces the amount of computation and gives the same results for many different cases
We consider quasi-single multifields (QSMF) Inflation [52], by following quasi-single field model [43,44,78,79], as an example to show how the diagrammatic method leads to relatively compact results compared to standard in-in formalism for three-point and four-point correlation functions of primordial scalar perturbations
Our results showed that the SK diagrammatic formalism has some advantages compared to the usual in-in formalism

Summary

Introduction

Investigating bispectrum, especially trispectrum based on in-in formulation is conducted comprehensively in recent works and articles about single-field models. Following this model, author in [52] has conducted multifield that contains abstruse mathematics. Besides this conventional calculating methods, reference author’s [78] used diagrammatic method and some methods based on Schwinger–Keldysh (SK) formalism [87,88,89] which greatly reduces the amount of computation and gives the same results for many different cases.

Diagrammatic rules and mixed propagator

Application to QSMF inflation and

Mixed propagator in QSMF model

Bispectrum

Trispectrua

Conclusions