Classical and Quantum Exact Solutions for a FRW Multiscalar Field Cosmology with an Exponential Potential Driven Inflation

J Socorro,Omar E Núñez,Rafael Hernández-Jiménez

doi:10.1155/2018/3468381

J Socorro, Omar E Núñez + Show 1 more

Open Access

https://doi.org/10.1155/2018/3468381

Copy DOI

Abstract

A flat Friedmann-Robertson-Walker (FRW) multiscalar field cosmology is studied with a particular potential of the form V(ϕ,σ)=V0e-λ1ϕ-λ2σ, which emerges as a relation between the time derivatives of the scalars field momenta. Classically, by employing the Hamiltonian formalism of two scalar fields (ϕ,σ) with standard kinetic energy, exact solutions are found for the Einstein-Klein-Gordon (EKG) system for different scenarios specified by the parameter λ2=λ12+λ22, as well as the e-folding function Ne which is also computed. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solved by applying an appropriate change of variables.

Highlights

The inflation paradigm is considered the most accepted mechanism to explain many of the fundamental problems of the early stages in the evolution of our universe [1,2,3,4], such as the flatness, homogeneity, and isotropy observed in the present universe
We studied a flat Friedmann-Robertson-Walker (FRW) multiscalar field cosmological model
We introduce the corresponding Einstein-Klein-Gordon (EKG) system of equations and the associated Hamiltonian density

Summary

Introduction

The inflation paradigm is considered the most accepted mechanism to explain many of the fundamental problems of the early stages in the evolution of our universe [1,2,3,4], such as the flatness, homogeneity, and isotropy observed in the present universe Another important aspect of inflation is its ability to correlate cosmological scales that would otherwise be disconnected. Even more the dynamical possibilities in multifield inflationary scenarios are considerably richer than in single-field models, such as in the primordial inflation perturbations analysis [22, 23] or the assisted inflation as discussed in [24], the general assisted inflation as in [21] In this sense the multiscalar fields’ cosmology is an attractive candidate to explain such phenomenon.

The Model

Classical Solutions

Quantum Solutions

Conclusions