Dynamics of Dirac-Born-Infeld dark energy interacting with dark matter

We study the dynamics of Dirac-Born-Infeld (DBI) dark energy interacting with dark matter. The DBI dark energy model considered here has a scalar field with a nonstandard kinetic energy term, and has potential and brane tension that are power-law functions. The new feature considered here is an interaction between the DBI dark energy and dark matter through a phenomenological interaction between the DBI scalar field and the dark matter fluid. We analyze two different types of interactions between the DBI scalar field and the dark matter fluid. In particular we study the phase-space diagrams of and look for critical points of the phase space that are both stable and lead to accelerated, late-time expansion. In general we find that the interaction between the two dark components does not appear to give rise to late-time accelerated expansion. However, the interaction can make the critical points in the phase space of the system stable. Whether such stabilization occurs or not depends on the form of the interaction between the two dark components.

Figure 1

Model I: The $x-y$ phase plane for the DBI dark energy interacting with dark matter. We have taken the parameters as $\beta =1$, ${\tilde{\lambda }}_1=1$, and $\tilde{\gamma }=0$. There are two stable, critical points: a(1) and a(2). Both points lead to accelerated expansion. The dotted line is $x=0$, which is the singularity value of the nonallowed region.

Figure 2

Model I: The $x-y$ phase plane for DBI dark energy interacting with dark matter with the parameters $\beta =1$, ${\tilde{\lambda }}_1=1$, and $\tilde{\gamma }=1$. The point ($b2$) is a stable critical point which leads to late-time accelerated expansion.

Figure 3

Model I: The $x-y$ phase plane for DBI dark energy interacting with dark matter with the parameters $\beta =-1$, ${\tilde{\lambda }}_1=1$, and $\tilde{\gamma }=1$. The point ($b2$) is a stable critical point which leads to late-time accelerated expansion.

Figure 4

Model II: The phase plane for the DBI dark energy with interaction to dark matter corresponding to $\alpha =1$ for ${\tilde{\lambda }}_1=1$, $\tilde{\gamma }=0$. The late-time attractors, (d3) and (d4), are stable fixed points which lead to accelerated expansion.