The way I see it, there is no end. We generally see the universe as a box wherein everything exists. where the box ends, the universe ends. Some might see it as a 4D sphere with us on the inside, but basically the same. How I see things, is as a 4D sphere, but instead of the things on the inside, they're on the outside.
Let's imagine a 2D person on a surface. He can only move on the surface, not upwards or downwards. Now, instead of just a person on this enormous surface, let's add some 'planets': discs (more or less). Our person can walk on it's 'surface' (the circle) and look 'up' and wonder about it's universe. It can even have it's own gravity, which works in the same way as our gravity (theories of relativity) but in 2D. As he gets smarter, he watches the skies and stars and other planets. One day, he decides to get of his disc of rock and go out into the universe. He goes forward and forward, he's following a straight line, perpendicular to the tangent of the circle he's living on. (It's obvious it's a circle: he always went straight ahead and returned to his point of origin) And as he's going farther away, he's seeing wonderful things, but (miraculously) he keeps following the same line. He thinks this plane is infinitely large: he's been travelling for 46.5 billion years at the speed of light (or at least very close to) and still he hasn't seen the end. But he keeps on continuing for another 46.5 billion years. One day, when he's looking out of his window, he sees a familiar blue dot. As it grows larger and larger, he's starting to realize this dot is his Earth, his home planet. He never thought it was possible, but the plane he was travelling on, wasn't a plane. it wasn't a disc as he thought. It was a sphere.
So this is how I believe it's put together. As a 3-sphere. On certain coordinates of this 3-sphere are planets, stars, comets... which fly according on a certain curve in this coordinate system. Just like we have a coordinate system here on Earth with our longitudes and latitudes, our 2D-guy has his system, but just with simple points on the circle (so he would say he's on coordinate 5, where we would say we're on 5,10). His people has thought of a similar coordinate system as they know, so it's based of the one they have on the planet. Once they realized that their planet was round, and not straight, and that outer space (or surface, whatever) is really large, they adjusted their coordinate system for outer space. They used concentric circles with the centre of their planet. And even when our brave traveller came back, it continued to work.
TL;DR: universe isn't cubic or spherical with us on the inside, but a 3-sphere with us on the outside.
Obviously, this is just my theory on the universe. I obviously can't make such observations myself. I did, however, think about it: everything in the universe is (near-)spherical. All things of 'importance' are on the OUTSIDE of those spheres. Why would the universe itself be such a different thing? Nature strives for consistency, it's only logical the universe would follow.
