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 \mathrel { \raise 1.29 pt \hbox { $ < $ \kern - 7.5 pt \lower 4.3 pt \hbox { $ \sim$ } } } w% \mathrel { \raise 1.29 pt \hbox { $ < $ \kern - 7.5 pt \lower 4.3 pt \hbox { $ \sim$ } } } -0.2 , or through collisional recombination for w \mathrel { \raise 1.29 pt \hbox { $ > $ \kern - 7.5 pt \lower 4.3 pt \hbox { $ \sim$ } } } -0.2 .
The radiation from e ^ { \pm } pair annihilation can not dominate over e ^ { \pm } , while that from proton decay will dominate over baryon and e ^ { \pm } for a while but not over dark matter .