  A new cosmological theory is proposed in the theoretical framework of
modified gravity theories which is based on a tachyonic field non-minimally
coupled with a specific topological invariant constructed with third order
contractions of the Riemann tensor. After proposing the action of the
cosmological model, the modified Friedmann relations and the Klein-Gordon
equations are obtained, describing the corresponding geometrical corrections to
the Einstein-Hilbert action. The physical features of the cosmological system
are investigated by adopting the dynamical system analysis in the case of an
exponential function for the geometrical coupling term. The investigation
revealed that the cosmological system can explain the current accelerated
expansion of the Universe and the matter dominated epoch, showing a high
compatibility to the recent history of our Universe for various values of the
coupling coefficients.
