Linear second-order differential equations for barotropic FRW cosmologies

TL;DR

This paper extends linear differential equations for barotropic FRW cosmologies using supersymmetry techniques, introducing an imaginary component to the adiabatic index linked to dissipation and instabilities.

Contribution

It introduces a novel supersymmetric approach connecting Dirac-like equations to FRW cosmologies, adding an imaginary part to the adiabatic index for modeling dissipation.

Findings

Extended the equations to include dissipation effects.

Linked imaginary adiabatic index to physical instabilities.

Provided a new mathematical framework for cosmological modeling.

Abstract

Simple linear second-order differential equations have been written down for FRW cosmologies with barotropic fluids by Faraoni. His results have been extended by Rosu, who employed techniques belonging to nonrelativistic supersymmetry to obtain time-dependent adiabatic indices. Further extensions are presented here using the known connection between the linear second-order differential equations and Dirac-like equations in the same supersymmetric context. These extensions are equivalent to adding an imaginary part to the adiabatic index which is proportional to the mass parameter of the Dirac spinor. The natural physical interpretation of the imaginary part is related to the particular dissipation and instabilities of the barotropic FRW hydrodynamics that are introduced by means of this supersymmetric scheme