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Of the universe? No, I don't think so.
There are upwards of 125 billion galaxies in our universe; let's assume the same is true of the DCU. If the Guardians have decided their universe into 3600 sectors, and since galaxies are, on the whole, rather evenly spread out, that means the average Green Lantern sector would contain...
34.7 million galaxies.
That's ... a lot of galaxies. Our galaxy, which is a fairly typical one, has about 100 billion stars. That would make the number of stars in a Green Lantern sector about...
34,700,000,000,000,000,000.
That's ... a lot of stars. But if they don't have planets with life on them, they don't really need policing, of course. How many life-bearing planets would there be to protect? Well, let's continue to assume our galaxy is typical.* Let's also assume there's (currently) no other life in our galaxy (which is conservative an estimate as you can get). Still, that would mean an average galaxy has one planet on it that's currently rocking with life. One life-bearing, protection-worthy planet per galaxies would mean at least...
34.7 million relevant planets in each Green Lantern sector.
That's ... a lot of planets. And it seems fair to say that the DCU is little more teeming with alien life than ours seems to be. So 34.7 million is a serious lowball estimate. Do you think DC wants us to imagine Green Lanterns as policing 34.7 million planets each? I don't think so.
DC; please don't call the Guardians the "Guardians of the Universe" any more. It's just stupid, and not in the same way that power rings and kryptonite meteors are. It's not "suspension of disbelief" stupid, it's "insulting the readers' intelligence" kind of stupid. Ignoring science is one thing; you need me to accept a Rainbow Brite "emotional power spectrum", sure, fine, no problem, sounds fun, and now I can have a powerful ring to color coordinate with any outfit. But ignoring math is something entirely different. I can swallow an internal logic for the DCU that is different from that of the real universe, but not one that's not really consistent with itself.
But please concede what it seems pretty clear you really mean: they are the Guardians of the Galaxy. They live at the center of the galaxy. Not the universe. The universe has no center (or, if you look at it another way, every point in the universe can be treated as its center, meaning that if you think you're the center of the universe, you're correct).
If the GLCorps protects the galaxy that means each sector has about 27 million stars in it and if, say, one in a million has life on it, that gives them each 27 life-bearing planets to take care of. That seems a little more in keeping with the GL stories I've read. And even that small number still would mean there's about 97,200 planets in New Earth's galaxy that support life!
*Yes, I know that not really true because of the large number of dwarf galaxies, but that only changes things by about 2 orders of magnitude. The point remains valid, even if you divide all the numbers used by 100.
