Dirac-like Equations for Barotropic Frw Cosmologies

where a is the scale factor of the universe, ρ and p are the energy density and the pressure, respectively, of the perfect fluid of which a classical universe is usually assumed to be made of, κ = 0,±1 is the curvature index of the flat, closed, open universe, respectively, and γ is the constant adiabatic index of the cosmological fluid. Recently, Faraoni, proposed the “Riccati route” of solving the system of eqs. (1)-(3) and Rosu used Faraoni’s approach to introduce a supersymmetric class of cosmological fluids possessing time-dependent adiabatic indices. It was claimed that these fluids can provide a simple explanation for a currently accelerating universe. In this work, we review the supersymmetric factorization methods for barotropic FRW cosmologies in section 2. Next, in section 3, we present Dirac-like (firstorder) coupled differential equations and their associated second-order differential equations and discuss them in a formal way.