Singularities and qualitative study in LQC

Abstract

We will perform a detailed analysis of singularities in Einstein Cosmology and in LQC (Loop Quantum Cosmology). We will obtain explicit analytical expressions for the energy density and the Hubble constant for a given set of possible Equations of State. We will also consider the case when the background is driven by a single scalar field, obtaining analytical expressions for the corresponding potential. And, in a given particular case, we will perform a qualitative study of the orbits in the associated phase space of the scalar. eld.