Cosmological evolution of the interacting phantom (quintessence) model in loop quantum gravity

The dynamics of the interacting dark energy model in loop quantum cosmology (LQC) is studied in this paper. The dark energy has a constant equation of state w_x and interacts with dark matter through a form 3cH(ρ_x+ρ_m). We find that for the quintessence model (w_x>-1) the cosmological evolution in LQC is the same as that in classical Einstein cosmology, whereas for phantom dark energy (w_x<-1), although there are the same critical points in LQC and classical Einstein cosmology, the loop quantum effect significantly reduces the parameter spacetime (c,w_x) required by stability. If parameters c and w_x satisfy the conditions that the critical points are existing and stable, the universe will enter an era dominated by dark energy and dark matter with a constant energy ratio between them, and accelerate forever; otherwise it will enter an oscillatory regime. Comparing our results with the observations we find at 1σ confidence level that the universe will accelerate forever.