Extended Phase Space Analysis of Interacting Dark Energy Models in Loop Quantum Cosmology
Résumé
The present work deals with the dynamical system investigation of interacting dark energy models (quintessence and phantom) in the framework of loop quantum cosmology by taking into account a broad class of self-interacting scalar field potentials. The main reason for studying potentials beyond the exponential type is to obtain additional critical points which can yield more interesting cosmological solutions. The stability of critical points and the asymptotic behavior of the phase space are analyzed using dynamical system tools and numerical techniques. We study two classes of interacting dark energy models and consider two specific potentials as examples: the hyperbolic potential and the inverse power-law potential. We find a rich and interesting phenomenology, including the avoidance of big rip singularities due to loop quantum effects, smooth and nonlinear transitions from matter domination to dark energy domination, and finite periods of phantom domination with dynamical crossing of the phantom barrier.
Mots clés
Loop quantum cosmology
self-interacting potentials
big rip singularity
Dark energy dark matter interaction
dark energy: interaction
quantum cosmology: loop space
phantom: crossing
critical phenomena: stability
phase space: analysis
singularity: big rip
effect: quantum
field theory: scalar
dynamical system
asymptotic behavior
quintessence
numerical methods
mathematical methods