Coincidence Problem in Cyclic Phantom Models of the Universe

TL;DR

This paper investigates cyclic phantom universe models to address the coincidence problem, showing that the universe spends significant time in states where matter and dark energy densities are comparable, similar to non-cyclic phantom models.

Contribution

It introduces a cyclic phantom model framework and calculates the fraction of time the universe remains in coincidental states, extending understanding of the coincidence problem in cosmology.

Findings

The fraction of time in coincidental states is comparable to non-cyclic phantom models.

Derived an explicit formula for the time fraction based on dark energy equation of state.

Shows the coincidence problem is alleviated in cyclic phantom scenarios.

Abstract

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})].