Whether the Universe is bounded or not is one of the great questions.
A lot depends on how much matter there is in it.
I think most of the smart money at the moment is on an unbounded Universe but it's far from certain.
One of the most interesting ideas is a finite unbounded Universe.
In the same way that if you travelled far enough in one direction on the surface of a sphere you would get back to the same place such a Universe would be the same but in 3D.
This would involve a Universe that is shaped like a 4 Dimensional Torus (ring doughut).
It's pretty hard to visualise but here's one represented in 2D
https://www.youtube.com/watch?v=nH9dFr3tGH4