Non-minimally coupled condensate cosmologies: a phase space analysis

We present an analysis of the phase space of cosmological models based on a non-minimal coupling between the geometry and a fermionic condensate. We observe that the strong constraint coming from the Dirac equations allows a detailed design of the cosmology of these models, and at the same time guarantees an evolution towards a state indistinguishable from general relativistic cosmological models. In this light, we show in detail how the use of some specific potentials can naturally reproduce a phase of accelerated expansion. In particular, we find for the first time that an exponential potential is able to induce two de Sitter phases separated by a power law expansion, which could be an interesting model for the unification of an inflationary phase and a dark energy era.