Thermodynamical properties of the Undulant Universe
  Recent observations show that our universe is accelerating by dark energy, so it is important to investigate the thermodynamical properties of it. The Undulant   Universe is a model with equation of state $\omega(a)=-\cos(b\ln a)$ for dark energy, where we show that there neither the event horizon nor the particle horizon exists. However, as a boundary of keeping thermodynamical properties, the apparent horizon is a good holographic screen. The Universe has a thermal equilibrium inside the apparent horizon, so the Unified First Law and the Generalized Second Law of thermodynamics are satisfied. As a thermodynamical whole, the evolution of the Undulant Universe behaves very well in the current phase. However, when considering the unification theory, the failure of conversation law at the epoch of the matter dominated or near singularity need some more consideration for the form of the Undulant Universe. 
Tian Lan, Tong-Jie Zhang, Bao-Quan Wang