We examine cyclic phantom models for the Universe, in which the universe is dominated sequentially by radiation, matter, and a phantom dark energy field, followed by a standard inflationary phase. Since this cycle repeats endlessly, the universe spends a substantial portion of its lifetime in a state for which the matter and dark energy densities have comparable magnitudes, thus ameliorating the coincidence problem. We calculate the fraction of time that the universe spends in such a coincidental state and find that it is nearly the same as in the case of a phantom model with a future big rip. In the limit where the dark energy equation of state parameter, $w$, is close to $-1$, we show that the fraction of time, $f$, for which the ratio of the dark energy density to the matter density lies between $r_1$ and $r_2$, is $f=-(1+w)\ln [(\sqrt{r_2}+\sqrt{1+r_2})/(\sqrt{r_1}+\sqrt{1+r_1})]$.

• Received 2 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.027303