Can dark energy evolve to the Phantom?

Abstract

Dark energy rapidly evolving from the dustlike state in the close past to the phantomlike state at present has been recently proposed as the best fit for the supernovae Ia data. Assuming that a dark energy component with an arbitrary scalar-field Lagrangian, which has a general dependence on the field itself and its first derivatives, dominates in the flat Friedmann universe, we analyze the possibility of a dynamical transition from the states with w>-1 to those with w<-1 or vice versa. We have found that generally such transitions are physically implausible because they are either realized by a discrete set of trajectories in the phase space or are unstable with respect to the cosmological perturbations. This conclusion is confirmed by a comparison of the analytic results with numerical solutions obtained for simple models. Without the assumption of the dark energy domination, this result still holds for a certain class of dark energy Lagrangians, in particular, for Lagrangians quadratic in field's first derivatives. The result is insensitive to topology of the Friedmann universe as well.

Figures (7)

• Figure 1: Possible phase curves in the neighborhood of the $\varphi-$axis. Only on the curves 1 and 6, the system crosses the $\varphi$ axis. Curves 2, 3, 4 and 7 have an attractor as a shared point with the $\varphi$ axis, whereas curves 5 and 8 have a repulsor. These attractors and repulsors can be fixed-point solutions or singularities.
• Figure 2: Phase curves in the neighborhood of the singular point $\Psi_{c}^{+}$ are plotted for the case of the real $\lambda$. At the points $\xi$, the solutions $\varphi(t)$ do not exist. These points together with $\Psi_{c}^{+}$ form the curve $\Gamma$ on which $\varepsilon_{,X}(\Gamma)=0$.
• Figure 3: Phase curves in the neighborhood of the singular point $\Psi_{c}^{+}$ are plotted for the case of the pure imaginary $\lambda$. Here we assume that the singular point is a focus.
• Figure 4: If $\mathbf{A}$ had the eigenvalues $\lambda_{1}=\lambda_{2}$, then the singular point $\Psi_{c}^{+}$ would be a nodal point and there would be a continuous set of trajectories passing through it. To illustrate this we plot here the phase curves in the particular case of a degenerate nodal point. The form of the equation of motion (\ref{['eq:Eq. of moution']}) excludes such types of singular points and therefore prevents the possibility of such transitions.
• Figure 5: The typical behavior of the phase curves in the neighborhood of the critical line where $K(\varphi)=0$ (here $\dot{\varphi}$ axis ) is plotted for the case when $K_{c}^{\prime}>0$ and $V_{c}^{\prime}<0$. Horizontal dashed lines are the analytically obtained separatrices $\dot{\varphi}_{\pm}$ and $(0,u_{\pm})$ are the points of transition.