Does Positronium Form in the Universe ?

Abstract

Positronium (the bound state of electron and positron) has been thought to be formed after proton decay ($>10^{34}$yr) through collisional recombination and then decays by pair annihilation, thereby changing the matter content of the universe. We revisit the issue of the formation of positronium in the long-term future of the universe in light of recent indication that the universe is dominated by dark energy and dark matter. We find that if the equation of state of dark energy $w$ is less than -1/3 (including the cosmological constant $w=-1$), then the formation of positronium would not be possible, while it is possible through bound-bound transitions for -1/3\siml w\siml-0.2, or through collisional recombination for w\simg-0.2. The radiation from \epm pair annihilation cannot dominate over \epm, while that from proton decay will dominate over baryon and \epm for a while but not over dark matter.Comment: 13 pages, to appear in JCA