A Grassmann Representation of the Hubble Parameter and the Cosmological Acceleration

The Riccati equation for the Hubble parameter H of barotropic FRW cosmologies in conformal time for κ 6= 0 spatial geometries and in comoving time for the κ = 0 geometry, respectively, is generalized to odd Grassmannian time parameters. We obtain a system of simple differential equations for the four supercomponents (two of even type and two of odd type) of the Hubble superfield function H that is explicitly solved. For the interesting physical case of flat cosmologies, we obtain cosmological acceleration in the second even Hubble component for all values of the adiabatic index.