Scalar field exact solutions for non-flat FLRW cosmology: A technique from non-linear Schr\"odinger-type formulation

TL;DR

This paper introduces a non-linear Schrödinger-type method for deriving exact solutions of scalar fields in non-flat FLRW cosmology, offering an alternative to standard approaches with insights into its advantages and disadvantages.

Contribution

The paper presents a novel NLS-type formulation for solving scalar field equations in non-flat FLRW universes, extending the toolkit beyond traditional methods.

Findings

Derived exact solutions for scalar fields in non-flat FLRW models.

Compared NLS formulation with standard Friedmann approach, highlighting differences.

Analyzed effective equations of state for phantom and non-phantom cases.

Abstract

We report a method of solving for canonical scalar field exact solution in a non-flat FLRW universe with barotropic fluid using non-linear Schr\"{o}dinger (NLS)-type formulation in comparison to the method in the standard Friedmann framework. We consider phantom and non-phantom scalar field cases with exponential and power-law accelerating expansion. Analysis on effective equation of state to both cases of expansion is also performed. We speculate and comment on some advantage and disadvantage of using the NLS formulation in solving for the exact solution.