MG11 
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Abstract

Non-singular solutions in Loop Quantum Cosmology

We will discuss non-singular solutions with scalar field in Loop Quantum Cosmology with a number of effective potentials: massless, massive scalar field, nonlinear self-interacting potential, cyclic, bicyclic potentials. General analysis with phase portrait technique will be presented. Such features of solutions as inflation and cyclic behavior will be considered.

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.We consider several of those models and derive cosmological equations for each of them. We also 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 $\Omega_m>2/3$ the equations describe Friedmannian Universe with the classical singularity at the beginning, while at $\Omega_m<2/3$ all solutions for the considered models start with zero density and non-vanishing scale factor. Even more remarkable, the value $\Omega_{sep}=2/3$, which defines the separatrix, is the same for all models. The latter reveales an underlying invariance hidden in the models, possibly, due to the basic nature of the GX-scaling.

Cavallo-Rees classification revisited

We revisit Cavallo and Rees classification given by the analysis of initial conditions in electron-positron-photon plasma which appears suddenly around compact astrophysical objects and gives origin to GRBs. We comment on each of the four scenarios proposed by Cavallo and Rees and discuss applicability of this diagram to describe evolution of GRB sources. We contrast this picture with the dynamical scenario which has been in the meantime identified in all GRB sources.