Non-linear Schr\"{o}dinger-type formulation of scalar field cosmology: two barotropic fluids and exact solutions

TL;DR

This paper develops a non-linear Schrödinger-type formulation for scalar field cosmology with two barotropic fluids, deriving exact solutions and suggesting the need for a time-dependent extension of the model.

Contribution

It introduces a novel time-independent NLS formulation for scalar field cosmology with two fluids and explores exact solutions, including a new one, for cosmological applications.

Findings

Seven exact solutions from previous work are analyzed.

One new exact solution is discovered and tested in cosmology.

The study indicates the necessity of extending to a time-dependent NLS formulation.

Abstract

Time-independent non-linear Schr\"{o}dinger-type (NLS) formulation of FRW cosmology with canonical scalar field are considered in case of two barotropic fluids. We derived Friedmann formulation variables in terms of NLS variables. Seven exact solutions found by D'Ambroise \cite{DAmbroise:2010dgl} and one new found solution are explored and tested in cosmology. The result suggests that time-independent NLS formulation of cosmology case should be upgraded to the time-dependent case.