|MadSci Network: Astronomy|
I follow your argument, but I don't agree 100% with it. Maybe 20%? You see, the reason it's hard for me to say absolutely yes or no is because astronomers are still figuring out much of the cosmology you're describing. Take your sentence, "If the matter is removed, the universe should take another shape." This may or may not be true! The answer could depend on a funny type of energy sometimes referred to as quintessence, and described as "a bizarre form of energy, possibly inherent in empty space" (Scientific American, 1998). If quintessence is out there, then the shape of the universe may actually be determined by quientessence instead of matter, or some combination thereof.
The current theory, however, comes from Einstein's theory of general relativity (GR). GR tells us that gravity and geometry are the same thing. This suggests that without matter, there would be no gravity, and hence, no curvature to our universe. But in our universe, GR indicates one of three geometries: saddle-shaped (AKA open), spherical (AKA closed) or flat.
The problem is that we don't know which of these geometries describe the shape of our universe (with the matter in it) with any sort of certainty. Consequently, many theories, including Hawking's, abound about the size and shape of the universe. As of today, there are just not enough data to rule in or out any of the theories suggested so far. However, once the shape of our universe is determined, we will be in a better position to answer your question about the shape of a massless universe. Come back and ask your question again, then!
Keep asking good questions,
[Moderator's Note: Everything Amber said is absolutely correct, but I just want to add that, in a universe without any matter OR "dark energy/quintessence," GR predicts that the universe would be saddle-shaped. That's sort of the default value. To learn more, you can check out Ned Wright's Cosmology Tutorial. Enjoy!]
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