Supernovae and Radio Galaxies Probing Gurzadyan-Xue Cosmological Models with Dark Energy

In the previous papers we derived cosmological equations for models with Gurzadyan-Xue dark energy, have performed their qualitative analysis and, particularly, have revealed a remarkable hidden invariance in the models with respect to the separatrix $\Omega_{sep}$ in their phase portraits. Now, new analytic solutions for these models are obtained, showing additional symmetries at various curvatures. The likelihood analysis with supernovae and radio galaxies data and their characteristics (age, the deceleration parameter), again demonstrate the crucial role of the $\Omega_{sep}$ for all models, in spite of the diversity of both, the initial equations and their solutions.