On the Schr\"odinger Equation for the Supersymmetric FRW Model

TL;DR

This paper develops a time-dependent Schr"odinger equation framework for the supersymmetric FRW cosmological model, incorporating a reparametrization-invariant action that modifies the constraint without altering the equations of motion.

Contribution

It introduces a reparametrization-invariant action into the supersymmetric FRW model, enabling a consistent Schr"odinger equation formulation.

Findings

Reparametrization-invariant action modifies the model's constraint.

The approach applies to both standard and supersymmetric FRW models.

The equations of motion remain unchanged by the new action.

Abstract

We consider a time-dependent Schr\"odinger equation for the Friedmann-Robertson-Walker (FRW) model. We show that for this purpose it is possible to include an additional action invariant under reparametrization of time. The last one does not change the equations of motion for the minisuperspace model, but changes only the constraint. The same procedure is applied to the supersymmetric case.