  In the present work, we study the cosmological model with fermionic field and
with the non-canonical kinetic term (f-essence). We also present some important
reductions of the model as well as its some generalizations. We also found the
exact solution of the model and examine the influence of such gravity-fermion
interaction on the observed accelerated expansion of our universe. Several
fermionic and bosonic-fermionic DBI models were constructed as some particular
reductions of f-essence and g-essence, respectively and their Chaplygin gas
counterparts are found. Finally, some nonlinear models of bouncing and cyclic
universes are proposed.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory