g-Essence as the cosmic speed-up

In the present work we analyze the g-essence model for the particular Lagrangian: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L=R+2[\alpha X^{n}+\epsilon Y-V(\psi,\bar{\psi})]$\end{document}. The g-essence models were proposed recently as an alternative and a generalization of the scalar k-essence models. We have presented the three types of the solutions for the g-essence model. We reconstructed the corresponding potentials and the dynamics of the scalar and fermionic fields according the evolution of the scale factor. The results show that the g-essence model predicts that our universe can be in both of the decelerated and accelerated expansion phases. In late time limit, we show that there is a family of exact solutions in which the free parameter may be remains in the range of m>−1. Further we discuss the existence of the de Sitter solutions in such a model.