Factorization approach for barotropic FRW model with a cosmological constant

TL;DR

This paper applies supersymmetric factorization to the Wheeler-DeWitt equation in a barotropic FRW cosmological model with a cosmological constant, deriving exact wave functions for specific parameter values.

Contribution

It introduces a supersymmetric factorization method for the Wheeler-DeWitt equation in barotropic FRW models, including the cosmological constant, and finds exact solutions for certain parameters.

Findings

Wave functions expressed as one-parameter families.

Exact solutions obtained for specific parameter values.

Method applicable to models with cosmological constant.

Abstract

We apply the technique of standard supersymmetric factorization for any q factor ordering in the Wheeler-DeWitt (WDW) equation for barotropic Friedmann-Robertson-Walker (FRW) minisuperspace model, including the cosmological term. The resulting wave functions of the universe are exhibited as one-parameter families, which for particular values of the $\gamma$ parameter of the barotropic model are exactly found.