Scalar field cosmology modified by the Generalized Uncertainty Principle
  We consider quintessence scalar field cosmology in which the Lagrangian of
the scalar field is modified by the Generalized Uncertainty Principle. We show
that the perturbation terms which arise from the deformed algebra are
equivalent with the existence of a second scalar field, where the two fields
interact in the kinetic part. Moreover, we consider a spatially flat
Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime (FLRW), and we derive the
gravitational field equations. We show that the modified equation of state
parameter $w_{GUP}$ can cross the phantom divide line; that is $w_{GUP}<-1$.
Furthermore, we derive the field equations in the dimensionless parameters, the
dynamical system which arises is a singular perturbation system in which we
study the existence of the fixed points in the slow manifold. Finally, we
perform numerical simulations for some well known models and we show that for
these models with the specific initial conditions, the parameter $w_{GUP}$
crosses the phantom barrier.
