A Model of the Universe including dark Energy
  In this work we explore a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field (with a double exponential self-interaction potential) and a cosmological constant. For a given region of the parameter space, our results confirm the possibility of a collapsing universe, which is necessary for an adequate definition of both perturbative quantum field and string theories. We have also reproduced the measurements of modulus distance from supernovae with good accuracy. 
Rolando Cardenas, Tame Gonzalez, Osmel Martin and Israel Quiros (Las   Villas Central University)