Cosmological dynamics of holographic dark energy with non-minimally coupled scalar field

Abstract

In this study, we consider FRW universe filled with matter, non-minimally coupling (NMC) scalar field under V(ϕ)=V0ϕ2 potential and holographic vacuum energy. Dark energy is contributed from both holographic vacuum energy and the NMC scalar field. NMC effective gravitational constant Geff(ϕ), is naturally defined at the action level. Therefore, the gravitational constant in the holographic vacuum density is an effective one, i.e. ρΛ=3c2/8πGeffL2. Apparent horizon is chosen as IR holographic cutoff scale as it is a trapped null surface. There are nine fixed points in this dynamical system with four independent dimensionless parameters. We consider flat case and find that viable cosmological evolution follows the sequence: an initial stiff-fluid-dominated phase, transitioning through a nearly dust-dominated era, and eventually reaching a stable dark energy-dominating state. Stability analysis requires that ξ<0 and 0 <0 and 0