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The paper studies a new type of dark energy, a scalar field with positive ornegative kinetic energy, generically coupled to a term which is composed byspecific contractions of the Riemann tensor. After presenting the resultingfield equations, we have analyzed the physical characteristics of thecorresponding model by implementing the linear stability theory. In the case ofan exponential coupling function and exponential potential energy we havededuced the phase space characteristics, analyzing the critical points obtainedwhich can represent specific eras in the evolution of the Universe. Theanalytical study is showing that this model can represent a feasiblecosmological setup, having various epochs which correspond to stiff-fluid,matter domination, and dark energy eras, pointing towards the emergence of theaccelerated expansion as a geometrical effect.

Dynamical aspects for scalar fields coupled to cubic contractions of the Riemann tensor