Classical and quantum exact solutions for a FRW in chiral like cosmology

TL;DR

This paper derives classical and quantum solutions for flat FRW cosmologies with two scalar fields, exploring models with single or dual potentials, including chiral field interactions, using Hamiltonian formalism.

Contribution

It provides exact classical and quantum solutions for two scalar field FRW models, including a chiral-like cosmology with mixed kinetic terms, which is a novel analytical approach.

Findings

Classical and quantum solutions for a single potential scalar field model.

Classical and quantum solutions for a chiral-like model with mixed kinetic terms.

Identification of quintom and quintessence-like cases within the chiral model.

Abstract

In this work, first, we study a flat Friedmann-Robertson-Walker Universe with two scalar fields but only one potential term, which can be thought as a simple quintessence plus a K-essence model. Employing the Hamiltonian formalism we are able to obtain the classical and quantum solutions. The second model studied, is also a flat Friedmann-Robertson-Walker Universe with two scalar fields, with the difference that the two potentials are considered as well as the standard kinetic energy and the mixed term (chiral field approach). Regarding this second model, it is shown that setting to zero the coefficient accompanying the mixed momenta term, two possible cases can be studied: a quintom like case ($m^{12}_{+}$) and a quintessence like case ($m^{12}_{-}$). For both scenarios classical and quantum solutions are presented.