Analysis cosmological tachyon and fermion model and observation data constraints

In this work we investigate a cosmological model with the tachyon and fermion fields with barotropic equation of state, where pressure $p$, energy density $\rho$ and barotropic index $\gamma$ are related by the relation $p=(\gamma-1)\rho$. We applied the tachyonozation method which allows to consider cosmological model with the fermion and the tachyon fields, driven by special potential. In this paper, tachyonization model was defined from the stability analysis and exact solution standard of the tachyon field. Analysis of the solution via statefinder parameters illustrated that our model in fiducial points with deceleration parameter $q = 0.5$ and statefinder $r = 1$ which corresponds to the matter dominated universe (SCDM) but, ends its evolution at a point in the future $(q =-1, \ r = 1)$ which corresponds to the de-Sitter expansion. Comparison of the model parameters with the cosmological observation data demonstrate, that our proposed cosmological model is stable at barotropic index $\gamma_0=0.00744$.