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In the present work, we study the cosmological model with fermionic field andwith the non-canonical kinetic term (f-essence). We also present some importantreductions of the model as well as its some generalizations. We also found theexact solution of the model and examine the influence of such gravity-fermioninteraction on the observed accelerated expansion of our universe. Severalfermionic and bosonic-fermionic DBI models were constructed as some particularreductions of f-essence and g-essence, respectively and their Chaplygin gascounterparts are found. Finally, some nonlinear models of bouncing and cyclicuniverses are proposed.

Cosmological models with non-canonical scalar and fermion fields: k-essence, f-essence and g-essence