  The paper proposes a novel cosmological model based on a two-field scenario,
where the two fields are independently coupled with a specific invariant, based
on cubic contractions of the Riemann tensor. After obtaining the modified
Friedmann equations and the specific Klein-Gordon relations, the investigation
studies the corresponding physical features by adopting the linear stability
theory in a quintom scenario case where the coupling functions and potential
energies have an exponential behavior. The corresponding investigation revealed
a high complexity of the phase space structure, with various stationary points
which can explain different aspects in the evolution of our Universe, the
matter dominated epoch, and the late time accelerated stage. The present model
can represent a viable solution to the dark energy problem due to the high
complexity of the phase space and the existence of the scaling solutions.
