KdV ADIABATIC INDEX SOLITONS IN BAROTROPIC OPEN FRW COSMOLOGIES

for the log derivative of the FRW scale factor, the famous Hubble parameterH(η) = da/dη a . The independent variable is the conformal time η, c is simply related to the adiabatic index of the cosmological fluid, c = 3 2 γ − 1 which was assumed constant by Faraoni, and κ = 0,±1 is the curvature index of the flat, closed, open FRW universe, respectively. For the mathematical considerations of this work we are more interested in the open cosmologies κ = −1. The flat case is special and has been discussed in a previous work, whereas the case κ = +1 will be commented in subsection 3.2 herein. We notice that from the mathematical point of view, Faraoni’s FRW Riccati equation being of constant coefficients is directly integrable. The solutions are