Falsifying Field-based Dark Energy Models
  We survey the application of specific tools to distinguish amongst the wide
variety of dark energy models that are nowadays under investigation. The first
class of tools is more mathematical in character: the application of the theory
of dynamical systems to select the better behaved models, with appropriate
attractors in the past and future. The second class of tools is rather
physical: the use of astrophysical observations to crack the degeneracy of
classes of dark energy models. In this last case the observations related with
structure formation are emphasized both in the linear and non-linear regimes.
We exemplify several studies based on our research, such as quintom and
quinstant dark energy ones. Quintom dark energy paradigm is a hybrid
construction of quintessence and phantom fields, which does not suffer from
fine-tuning problems associated to phantom field and additionally it preserves
the scaling behavior of quintessence. Quintom dark energy is motivated on
theoretical grounds as an explanation for the crossing of the phantom divide,
i.e. the smooth crossing of the dark energy state equation parameter below the
value -1. On the other hand, quinstant dark energy is considered to be formed
by quintessence and a negative cosmological constant, the inclusion of this
later component allows for a viable mechanism to halt acceleration. We comment
that the quinstant dark energy scenario gives good predictions for structure
formation in the linear regime, but fails to do that in the non-linear one, for
redshifts larger than one. We comment that there might still be some degree of
arbitrariness in the selection of the best dark energy models.
