Global existence of solutions is proved, in the case of a positive cosmological constant and positive initial velocity of the cosmological expansion factor on the three types of Friedman- Robertson-Walker space-time, and asymptotic behavior is investigated.
"Global solutions to the Einstein equations with cosmological constant on the Friedman-Robertson-Walker space times with plane, hyperbolic, and spherical symmetries." Commun. Math. Sci. 6 (3) 595 - 610, September 2008.