New dynamical features of pure k-essential cosmologies

We come back on the dynamical properties of k-essential cosmological models and show how the interesting phenomenological features of those models are related to the existence of boundaries in the phase surface. We focus our attention to the branching curves where the energy density has an extremum and the effective speed of sound diverges. We discuss the behaviour of solutions of a general class of cosmological models exhibiting such curves and give two possible interpretations; the most interesting possibility regards the arrow of time that is reversed in trespassing the branching curve. This study teaches to us something new about general FLRW cosmologies where the fluids driving the cosmic evolution have equations of state that are multivalued functions of the energy density and other thermodynamical quantities.