Abstract
In the present work, we study the cosmological model with fermionic field and with the non-canonical kinetic term ( f-essence ). We present some important reductions of the model as well as some of its generalizations. We also find the exact solution of the model and examine the influence of such gravity-fermion interaction on the observed accelerated expansion of our universe. Further, we discuss the cosmological implications of the exact models. We show that our f-essence model corresponds to ΛCDM, but not a standard cold dark matter model containing no radiation. Also, our particular f-essence model has no Einstein's static universe. Further we discuss several fermionic Dirac-Born-Infeld (DBI) models as some particular reductions of f-essence, respectively and their Chaplygin gas counterparts are found.