A Cosmological Model with Dark Spinor Source

In this paper, we discuss the system of Friedman-Robertson-Walker metric coupling with massive nonlinear dark spinors in detail, where the thermodynamic movement of spinors is also taken into account. The results show that, the nonlinear potential of the spinor field can provide a tiny negative pressure, which resists the Universe to become singular. The solution is oscillating in time and closed in space, which approximately takes the following form $$g_{\mu \nu }={\bar{R}}^2(1-\delta \cos t{)}^2\text{diag}(1,-1,-{\sin }^{2}r,-{\sin }^{2}r{\sin }^2\theta ),$$ with $\bar{R}=(1\sim 2)\times {10}^{12}$ light year, and $\delta =0.96\sim 0.99$. The present time is about $t\sim {18}^{\circ }$.