Monsieurrenard, it is understood by most that the expansion of the universe and the big bang isn't just matter being launched, like an explosing, into the void of space around it. No, the universe itself expanded, like a balloon. The 'big bang' is no explosion. The expansion of the universe means that the spaces betwene all points in the universe is getting bigger. Space-time itself is expanding. Matter isn't launced through space-time, away from the point of the big bang.
The shape of the universe is often thought to be a saddle. But like I said, the nature of the geometry of the universe is not know. So the shape is also unknown.
As for peer-reviewed sources, actually I did read something about the shape of the universe in Scientific American. But that is a popular science magazine. Since I am not a cosmologist I don't really know peer reviewed sources or other academic sources. But as far as I know the views I presented are some of the mainstream ideas on the subject.
There are two different universe we can comment on. The observable universe and the universe as a whole. The observable universe is has a radius of 13,7 million lightyears, so the light, representing the universe, that has been able to reach earth in the time the universe has existed.
But the shape of the universe itself as a whole is more problametic. It is now believed, at least by some, that the unverse can actually be much much, I really mean, much bigger than that what we are able to observe. But that doesn't mean it is infinite.