Dynamics of interacting phantom scalar field dark energy in loop quantum cosmology

We study the dynamics of a phantom scalar field dark energy interacting with dark matter in loop quantum cosmology. Two kinds of coupling of the form $\alpha {\rho }_m\dot{\varphi }$ (case I) and $3\beta H({\rho }_{\varphi }+{\rho }_m)$ (case II) between the phantom energy and dark matter are examined with the potential for the phantom field taken to be exponential. For both kinds of interactions, we find that the future singularity appearing in the standard Friedmann-Robertson-Walker cosmology can be avoided by loop quantum gravity effects. In case II, if the phantom field is initially rolling down the potential, the loop quantum effect has no influence on the cosmic late time evolution and the universe will accelerate forever with a constant energy ratio between the dark energy and dark matter.

Figure 1

The stability regions of $(\lambda ,\beta )$ parameter space for case II. In LQC, in the region I the rolling-down critical point (point C) is a stable late time attractor; in region II there are no stable critical points. However, in the standard FRW cosmology, in the region I, both the climbing-up scaling solution and the rolling-down scaling solution are the stable late time attractors, while in the region II, the climbing-up solution is the stable late time attractor. III represents the region of the solutions without physical meaning.

Figure 2

The evolution of $H$ for a climbing-up phantom field with different coupling constants ($\beta =0.2$, 0.8) and $\lambda =1$, $V_0=1$, ${\rho }_c=1.5$, ${\dot{\varphi }}_0=-0.4$ in case II.

Figure 3

The evolution of cosmic total energy density for a climbing-up phantom field with different coupling constants ($\beta =0.2$, 0.8) and $\lambda =1$, $V_0=1$, ${\rho }_c=1.5$, ${\dot{\varphi }}_0=-0.4$ in case II.

Figure 4

The convergence of different initial conditions to the attractor solution in the $(x,y,z)$ phase space for a rolling-down phantom field in case II. The red point denotes the critical point C.

Figure 5

The evolution of $H$ with time for a rolling-down phantom field with $\beta =0.2$, $\lambda =1$, $V_0=1$, ${\rho }_c=1.5$, and ${\dot{\varphi }}_0=0.4$.

Figure 6

The evolution of the effective equation of state for the total cosmic energy in a rolling-down phantom model with $\beta =0.2$, $\lambda =1$, $V_0=1$, ${\rho }_c=1.5$, and ${\dot{\varphi }}_0=0.4$.

Figure 7

The evolutionary curves of the fractional densities of a phantom field (dashed line) and dark matter (solid line) for a rolling-down phantom model with $\beta =0.2$, $\lambda =1$, $V_0=1$, ${\rho }_c=1.5$, and ${\dot{\varphi }}_0=0.4$.