  The paper studies a new type of dark energy, a scalar field with positive or
negative kinetic energy, generically coupled to a term which is composed by
specific contractions of the Riemann tensor. After presenting the resulting
field equations, we have analyzed the physical characteristics of the
corresponding model by implementing the linear stability theory. In the case of
an exponential coupling function and exponential potential energy we have
deduced the phase space characteristics, analyzing the critical points obtained
which can represent specific eras in the evolution of the Universe. The
analytical study is showing that this model can represent a feasible
cosmological setup, having various epochs which correspond to stiff-fluid,
matter domination, and dark energy eras, pointing towards the emergence of the
accelerated expansion as a geometrical effect.
