Who's the man with the raspy voice? We're honestly asking here.
(Why else would we call him "the man with the raspy voice"? It was either that or go with some dad-level pun like "Rasputin.")
Put as clearly as possible, the man with the raspy may or may not be an invention of Cole's mind. He is so enigmatic that he even offers the possibility of his own fictitiousness:
MAN WITH RASPY VOICE: Maybe means maybe I'm in the next cell. Another volunteer like you. Or maybe I'm in the Central Office, spying on ya for all those science bozos. Or hey, maybe I'm not even here. Maybe I'm just in your head. No way to confirm anything.
No way, indeed.
The man speaks to Cole—either through the vents or in Cole's head—during Cole's various recoveries in the year 2035. He taunts Cole and offers him advice in equal measure. If he is a real person, then his goal appears to be to guide Cole, either in line with the Scientists' goals or to obstruct them. We can't say for certain.
If he's an invention of Cole's mind, then his purpose is to be a personification of Cole's inner conflict. When Cole says he doesn't know what he wants, for example, the man with the raspy voice replies that he knows exactly what Cole wants. That is,
MAN WITH RASPY VOICE: To be topside. Breath the air. To be with…her. Isn't that right? Isn't that what you want? Bob?
Immediately after this conversation, Cole hatches his plan to trick the scientists into sending him back in time so he can be with Dr. Railly.
So it seems likely that the man is a part of Cole's fractured personality, and their conversations are Cole's way of sorting out his own mind. Basically, he's talking to himself.
Now, we hear some of you asking, "But what about that homeless man in 1996?" While it is true that the homeless man sounds a lot like the man with the raspy voice, there is no way to know if they are the same guy. The homeless guy tells Cole that they have a tracking device in his teeth. But when Cole talks to him directly, he shirks away, frightened, as though he doesn't know Cole.
Later, in 2035, the man with the raspy voice contradicts the homeless man from 1996:
COLE: I saw you…in 1996, in the real world. You pulled out your teeth.
MAN WITH RASPY VOICE: Why would I pull out my teeth, Bob? That's a no-no. And when did you say you saw me? In 1872?
But it is also entirely possible the two are the same person, and like a typical time-traveler in 12 Monkeys, he has become unhinged and mentally fragmented across the timeline.
Of course, we know you've come here seeking answers, something solid to ground your conversations on when talking about 12 Monkeys. Lucky for you, we've got one a solid fact: this guy could use a throat lozenge. Sorry if that's a bit underwhelming, but when it comes to this character, that's about as solid as any fact can be.