Hidden invariance in Gurzadyan-Xue cosmological models

The dark energy formula derived by Gurzadyan and Xue which leads to a value fitting the SN data, provides a scaling relation between physical constants and cosmological parameters and defines a set of cosmological models. In previous works we considered several of those models and derived cosmological equations for each of them. In this Letter we present the phase portrait analysis of those models. Surprisingly, we found that the separatrix in the phase space which determines the character of solutions depends solely on the value of the current matter density, namely: at Ωm>2/3 the equations describe Friedmannian Universe with the classical singularity at the beginning, while at Ωm<2/3 all solutions for the considered models start with zero density and non-vanishing scale factor. Even more remarkable, the value Ωsep=2/3, which defines the separatrix, is the same for all models. The latter reveals an underlying invariance hidden in the models, possibly, due to the basic nature of the GX-scaling.