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A flat Friedmann-Robertson-Walker (FRW) multiscalar field cosmology is studied with a particular potential of the form

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 [

The single-field scalar models have been broadly used to describe the primordial expansion, the most phenomenological successful are those with a quintessence scalar field and slow-roll inflation [

Recent works have shown that multiscalar field models are very fruitful when studying the early stages of the universe, such as the case in [

Indeed the multiscalar field models for inflation are of interest even on most recent studies, such as the above-mentioned cases; however, one of the most important features in such models is the potential associated with the scalar fields, and in many cases, the employed potentials are simple polynomial powers of the scalar fields or in other cases the employed potential is a series of lineally summed exponentials; however, it has been shown that a potential of the form

Generally, in the studies of inflationary cosmology one employs the usual slow-roll approximation with the objective to extract simple expression for basics observable, such as the scalar and tensor spectral indices, the running of the scalar spectral index, and the tensor-to-scalar ratio. Moreover, in the slow-roll regime the set of EKG equations reduces in such a way that one can quickly obtain the solution of the scale factor. Nevertheless, there is an alternative approach which allows for an easy derivation of many inflation results. It is called Hamilton’s formulation, widely used in analytical mechanics. Using this method we obtain the exact solutions of the complete set of EKG equations without using the aforementioned approximation.

On the other hand, we implement a basic formulation in quantum cosmology by means of the Wheeler-DeWitt (WDW) equation. The WDW equation has been analyzed with different approaches in order to solve it, and there are several papers on the subject, such is the case in [

This work is arranged as follows. In Section

We begin with the construction of two scalar fields cosmological paradigm, which requires canonical scalar fields

By building the corresponding Lagrangian and Hamiltonian densities for this cosmological model, classical solutions to Einstein-Klein-Gordon equations ((

We start from the Hamilton equations (

Having

For this case

For this case we modify the relation between the momenta equation (

Inflation is characterised by the number of e-folds it expands during such period that corresponds to

At the end of inflation the expansion rate of the scale factor must be null which translates to

Computation of the number of e-folds

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The Wheeler-DeWitt equation for this model is acquired by replacing

The solution of (

For this case, (

For this case, (

Whilst

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. Exact solutions to the EKG system are derived by means of Hamilton’s approach where a particular scalar potential of the form

No data were used to support this study and all required information to arrive to the findings of this work is included within the article.

The authors declare that they have no conflicts of interest.

This work was partially supported by CONACYT 167335 and 179881 grants and PROMEP grants UGTO-CA-3. Rafael Hernández-Jiménez acknowledges CONACYT for financial support. This work is part of the collaboration within the Instituto Avanzado de Cosmología. Many calculations were done by Symbolic Program REDUCE 3.8.