Watching Cortana, you can tell she's troubled or posessed. She's had a lot of time to mingle with Gravemind since we last saw her in H2. Little is known about Gravemind, and that leads to a disturbing situation. Has "he" somehow corrupted Cortana? Have their minds joined together? In the sequence that leads into this screen capture, we see her eye roll down, from the back of her head. Something is definitely happening there.

Also, thinking to Cortana's speech: "I have defied gods and demons." If you stick with the dual personality idea, it makes sense that Gravemind would be speaking through her. I don't recall the exact words in H2, but I do remember him saying he's been around forever. Defying gods (living an abnormally long time,) and defying demons (surviving Master Chief's rampant destruction.)

It only makes sense that somehow they have linked. Otherwise, what drives that arc in the plot? If you remove the conflict it just becomes "oo, Cortana is far away. Why not just go get her?" As of now it's "Oh damn, that crazy plant from Little Shop of Horrors has pulled off a Vulcan mind meld with her. Let's break out the guns!"