As we all KNOW... or if not I'll summarize it anyway.
The Covenant destroyed the majority of the human race's Colonized worlds and left a path of destruction in their wake.
Masterchief aka Spartan-117 aka John-117 aka Johnson's best friend and a handful of his buddies and Spartan-IIs saved them all pretty much.
They ended up destroying Two Halos I believe as the one in Halo 2 was not destroyed I don't think, and the Ark.
The Ark was the Lesser Ark and compared to the Greater Ark, was pretty useless, though it did create all of the smaller Halos.
The Greater Ark Created the larger Halos.
(Theoretically in my brain, I believe Requiem may be the Greater Ark.)
RANDOMNESS SET ASIDE:
The Halo 4 Antagonists are not the Covenant as they were destroyed in the First trilogy.
The Halo 4 Antagonists are Prometheans. Though not the Promethean Warrior-Servant 'Caste' from the Forerunner Saga. Originally the Prometheans were the greatest and Earliest Forerunners alive. The Didact was one of these, Assuming they were created by the 'New didact named; Bornstellar' as a means of defence for his apparent 'Cryptum' and Requiem itself. Which may well be the Greater Ark.
The Greater Ark may have closed and became a 'Shield-World' so to speak. It's plausible and there is no evidence saying that it couldn't do that.
The Prometheans that will be seen in Halo 4 and possibly throughout the new 'Reclaimer Trilogy' are simply Heavily Advanced Forerunner AI.
When I state advanced I mean... Sentinel = Ball of Flying Scrap compared to the Promethean's
SO THIS WAS MEANT TO CLARIFY WHAT PROMETHEANS ARE IN HALO 4