Coincidence Problem in an Oscillating Universe
  We analyze an oscillating universe model in brane world scenario. The oscillating universe cycles through a series of expansions and contractions and its energy density is dominated by dust matter at early-time expansion phase and by phantom dark energy at late-time expansion phase. We find that the period of the oscillating universe is not sensitive to the tension of the brane, but sensitive to the equation-of-state parameter $w$ of the phantom dark energy, and the ratio of the period to the current Hubble age approximately varies from 3 to 9 when the parameter $w$ changes from -1.4 to -1.1. The fraction of time that the oscillating universe spends in the coincidence state is also comparable to the period of the oscillating universe. This result indicates that the coincidence problem can be significantly ameliorated in the oscillating universe without singularity. 
Guangcan Yang and Anzhong Wang