arXiv2010
In this paper, we investigate the quintessence models with an oscillating equation of state (EoS) and their potentials. From the constructed potentials, which have the EoS of $ω_ϕ=ω_0+ω_1\sin z$, we find they are all the oscillating functions of the field $ϕ$, and the oscillating amplitudes are decreasing (or increasing) with $ϕ$. From the evolutive equation of the field $ϕ$, we find this is caused by the expansion of the universe. This also makes that it is very difficult to build a model whose EoS oscillates forever. However one can build a model with EoS oscillating for a period. Then we discuss three quintessence models, which are the combinations of the invert power law functions and the oscillating functions of the field $ϕ$. We find they all follow the oscillating EoS.