Phantom expansion with non-linear Schr\"{o}dinger-type formulation of scalar field cosmology

TL;DR

This paper reformulates non-flat scalar field cosmology using a non-linear Schrödinger-type approach, analyzing phantom expansion and scalar field solutions, revealing that phantom behavior can occur even with effective equations of state above -1.

Contribution

It introduces a non-linear Schrödinger-type formulation for non-flat scalar field cosmology, providing new insights into phantom expansion and exact solutions in this framework.

Findings

Phantom expansion can occur even with $w_{eff} > -1$ in non-flat universes.

In open universes, phantom expansion is possible with $w_{eff} > 0$.

The paper provides scalar field exact solutions in both Friedmann and NLS formulations.

Abstract

We describe non-flat standard Friedmann cosmology of canonical scalar field with barotropic fluid in form of non-linear Schr\"{o}dinger-type (NLS) formulation in which all cosmological dynamical quantities are expressed in term of Schr\"{o}dinger quantities as similar to those in time-independent quantum mechanics. We assume the expansion to be superfast, i.e. phantom expansion. We report all Schr\"{o}dinger-analogous quantities to scalar field cosmology. Effective equation of state coefficient is analyzed and illustrated. We show that in a non-flat universe, there is no fixed $w_{\rm eff}$ value for the phantom divide. In a non-flat universe, even $w_{\rm eff} > -1$, the expansion can be phantom. Moreover, in open universe, phantom expansion can happen even with $w_{\rm eff} > 0$. We also report scalar field exact solutions within frameworks of the Friedmann formulation and the NLS formulation in non-flat universe cases.