  We study in some detail an interacting cosmological model based on two
canonical scalar fields starting from a Lagrangian description. Contrary to
other more phenomenological approaches where non-relativistic matter and dark
energy are cosmological perfect fluids, and where a source term is added by
hand at the level of the continuity equations, here within Einstein's theory we
model the dark sector, which dominates the evolution of the universe, as two
minimally coupled scalar fields, out of which the first play the role of dark
matter and the second plays the role of dark energy. We compute both the
deceleration parameter and the distance modulus versus red-shift, and we
demonstrate that the model is capable of explaining the current cosmic
acceleration. We find that a negative coupling constant implies two distinctive
features, which comprise two robust predictions of the model studied in the
present work, and which are the following: a) a transient acceleration phase,
and b) a collapsing Universe, or in other words an initial expansion which is
followed by a contraction leading eventually to a Big-Crunch.
