Korteweg-de Vries adiabatic index solitons in barotropic open FRW cosmologies

Applying standard mathematical methods, it is explicitly shown how the Riccati equation for the Hubble parameter H(\eta) of barotropic open FRW cosmologies is connected with a Korteweg-de Vries equation for adiabatic index solitons. It is also shown how one can embed a discrete sequence of adiabatic indices of the type n^2({3/2}\gamma -1)^2 (\gamma \neq 2/3) in the sech FRW adiabatic index solitonComment: 5 pages, without figure

Darboux class of cosmological fluids with time-dependent adiabatic indices

A one-parameter family of time dependent adiabatic indices is introduced for any given type of cosmological fluid of constant adiabatic index by a mathematical method belonging to the class of Darboux transformations. The procedure works for zero cosmological constant at the price of introducing a new constant parameter related to the time dependence of the adiabatic index. These fluids can be the real cosmological fluids that are encountered at cosmological scales and they could be used as a simple and efficient explanation for the recent experimental findings regarding the present day accelerating universe. In addition, new types of cosmological scale factors, corresponding to these fluids, are presentedComment: document with the following three latex files: 1) quhm.tex: 17 pages, 10 figs, 16 numbered refs, Honorable Mention GRF 2000, 2) errad.tex: Errata and Addenda (EaA) of 5 pages with 2 figs enclosed, 3) analogy.tex: Negative friction of Darboux cosmological fluids of 4 page

Supersymmetry of FRW barotropic cosmologies

Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K =0Comment: 6 page