Qualitative dynamical properties of a spatially closed FRW universe conformally coupled to a scalar field

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Abstract
In this work the dynamics of a spatially closed Friedmann-Robertson-Walker model for the universe conformally coupled to a scalar field is studied. It is proven that this dynamics, formulated in terms of the proper time t (or cosmic time) is very simple. For arbitrary initial conditions, we prove that the universe will ultimately collapse in a finite time. We also show that there is no inflation at any stage of the evolution. When represented in phase space all trajectories of the system are unbounded, owing to a divergence that appears at the singularity, and showing that there is no chaos.

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