Bianchi type I anisotropic power-law solutions for the Galileon models

We will study the cosmological solutions of a class of Galileon models. A special class of the Bianchi type I power-law solutions will be presented in this paper. We will show that these Bianchi type I power-law solutions are stable during the inflationary phase. In addition, we will also show that the presence of a phantom field induces at least an unstable mode for the perturbation equation and destabilizes the power-law solutions.

Figure 1

The anisotropic fixed point with the field parameters chosen as $\lambda =0.1$, $\rho =50$, and $k_0=-3{\rho }^2/2$ is shown as attractor solutions in this figure. All trajectories in the phase space of $X$, $Y$, and $Z$, with different initial conditions converge to the anisotropic fixed point (plotted as the purple point). The initial conditions $[X(t=0),Y(t=0),Z(t=0)]$ are set as (0.1, 0.45, 0.2) for the thin solid red curve, (0.15, 0.5, 0.15) for the thick solid blue curve, and (0.2, 0.5, 0.2) for the green dotted curve, respectively.