In this work, we propose a new dark energy cosmological model, by considering a new quintom scenario which is based on the superposition between a quintessence scalar field and a noncanonical scalar field, both nonminimally coupled with cubic self-interaction terms. Considering that the two scalar fields of the quintom construction are nonminimally coupled in an independent manner with cubic self-interactions terms in the corresponding action, we have analyzed the dynamical features of the present model in the phase-space. By performing a dynamical system analysis in the case of exponential potentials, we have analyzed the structure of the phase-space, obtaining different possible constraints for the parameters of the model which correspond to distinct evolution scenarios.

The paper extends basic Einstein--Hilbert action by adding an invariant constructed from a specific contraction between the Einstein tensor and the energy momentum tensor, encoding a non--minimal coupling between the space--time geometry and the matter fields. The fundamental Einstein--Hilbert action is extended by considering a generic function ${f}(R,G_{\mu \nu}T^{\mu \nu})$ which is further decomposed into its main constituents, a geometric component which depends on the scalar curvature, and a second element embedding the interplay between geometry and matter fields. Specific cosmological models are established at the level of background dynamics, based on particular couplings between the matter energy--momentum tensor and the Einstein tensor. After deducing the resulting field equations, the physical aspects for the cosmological model are investigated by employing a dynamical system analysis for various coupling functions. The investigation showed that the present model is compatible with different epochs in the evolution of our Universe, possible explaining various late time historical stages.

No abstract