Quintessence models with an oscillating equation of state and their potentials

In this paper, we investigate the quintessence models with anoscillating equation of state (EOS) and its potentials. From theconstructed potentials, which have an EOS of$omega_{phi}=omega_0+omega_1sin z$, we find that they are allthe oscillating functions of the field $phi$, and the oscillatingamplitudes decrease (or increase) with $phi$. From the evolutiveequation of the field $phi$, we find that this is caused by theexpansion of the universe. This also makes it very difficult tobuild a model whose EOS oscillates forever. However one can build amodel with EOS oscillating for a certain period of time. Then wediscuss three quintessence models, which are the combinations of theinvert power law functions and the oscillating functions of thefield $phi$. We find that they all follow the oscillating EOS.