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The Quintessence With Oscillating State Equation and Its Potential

In this paper, I discuss the quintessence with oscillating state equation and the function form of its potential. From the constructed potential, which has the state equation ωφ = w0 +w1 sin z, I find it is also an oscillating function, but the oscillating amplitude is decreasing (increasing) with the field. From the evolution equation of the field φ, I find which is for the effect of the cosmic expansion is the resistant to the kinetic energy of the field φ. Also for this reason, it is very difficult to build a potential which can follow the state equation oscillating forever. But it is easy to build a model with state equation being oscillating for a period. Then we discuss three models of the quintessence with potentials, which are the combinations of the invert power law function and the oscillating function of the field φ. I find that they all indeed give the oscillating state equation. PACS numbers: 98.80.Cq, 98.80.Bp, 04.90.+e