I believe that, in the context of what the shell is supposed to do, the Cosmos Shell is bugged/broken.
I purchased the shell with my Titan and had it equipped when doing Flashpoint, Crucible and Nightfall. At the time, I believe it was actually adding 10% XP to my Titan but I'm not totally sure about it.
When I switched to my Hunter, I gave that character the same shell and started running Heroic Strikes. However, I didn't seem to be leveling-up as quickly as my Titan had been. So, in the middle of a strike, I unequipped the Cosmos Shell and equipped a shell that doesn't effect my XP gains at all.
With the shell equipped, I killed a Vex Goblin and the XP went up 75. When I removed it, I killed another Vex Goblin (not orange or yellow health bar, both just normal red bars) and it was still 75. My friend that I was running these Strikes with had also purchased the Cosmos Shell and he never changed character. When I unequipped the shell and told him it was still 75, he still had the shell equipped and he told me his said 75, too.
Anyone able to look into this and see if, in fact, this shell is currently broken? This was on the Xbox One, by the way, in case it is a bug that's effecting just one console.