Universe expansion is slowing down

Myslius, the universe has been accelerating since approximately 7 billion years after the big bang. NOT since the big bang itself. In fact, it was decelerating until roughly the 7 billion year mark. At that time, the density of dark energy (the cosmological constant, so it probably doesn't ever lose density) overcame the density of matter/dark matter, which falls very fast.

The Expanding Universe: From Slowdown to Speed Up
Distant supernovae are revealing the crucial time when the expansion of the universe changed from decelerating to accelerating


Currently the density of dark energy is higher than that of matter, but in the distant past the density of matter should have been greater, so the expansion should have been slowing down then.
http://www.scientificamerican.com/ar...ws-then-speeds

According to theorists, if the universe is absolutely flat, the matter density of the universe is, and always will be, equal to its critical density since the end of the inflationary epoch.