  In this work we present a model of the universe in which dark energy is
modelled explicitely with both a dynamical quintessence field and a
cosmological constant. Our results confirm the possibility of a future
collapsing universe (for a given region of the parameter space), which is
necessary for a consistent formulation of string theory and quantum field
theory. We have also reproduced the measurements of modulus distance from
supernovae with good accuracy.
