The definition of the universe that I'm accustomed to is "all matter and energy, including the earth, the galaxies, and the contents of intergalactic space, regarded as a whole." I can see where this definition might be simplified into "everything in reality." However, the question we must then is ask is what is reality? Science has yet to discover if there is an end to space. Perhaps space (and thus reality) go on forever and ever. If the universe is infinite, then there is no edge to universe and thus no end to reality. If the universe if finite, it could have an edge. However, I'm not sure there is such a direct correlation between the type of reality you are discussing and the physical universe.
Maybe others can provide a more informed answer to this question, but, as I understand it, the defintion of the universe is not "everything in reality". The universe is defined, rather, as "all knowable and related space-time", or something along those lines.
This means that multiple universes can possibly exist, separate from one another, which is something that string theory apparently suggests.
I don't know all the details on this. Hopefully some more folks will chime in to help with this question. In the mean time, you might be interested in looking into the idea of the "multiverse":
The multiverse (or meta-universe, metaverse) is the hypothetical set of multiple possible universes(including the historical universe we consistently experience) that together comprise everything that exists and can exist: the entirety of space, time,matter, and energy as well as the physical laws and constants that describe them.
However, the notion of mutiple universes may be beside the point if your question really is simply, "Does reality end with the limits of physical space?"
In that case, I believe the answer, scientifically, is yes. Theologically, there are all sorts of answers that would propose, essentially, to say "no". Theologically, reality is not necessarily bound by the limits of physical space (in one universe or a multiplicity of universes).
Nothing is something, due to the fact that "nothing" is a word created by humans, therefore making it something.
Therefore i think there is no edge to the universe.
My comment in "the middle of the Universe applied here to.
The spherical (or solid oval) universe that we imagine is a 3-Sphere different from our ordinary 2-sphere of daily life ! A 2-sphere has 2 angles on it, latitude and longitude, but a 3-sphere has 3-angles, and along the radius of this 3-sphere runs the time-axis ! Now let me explain the non-trivial point,
Surface of this 3-sphere that is our universe actually contains all the matter and space itself... time runs perpendicular to this surface that is along the radius. Now this surface is not usual 2D surface but a 3D surface as its a 3-sphere and this surface is the universe that we can see around us, though it doesn't appear to us as a surface as we cannot sense 4-Dimension but we can only sense 3D. Nosw if the whole universe lives on the surface, then does this question has a menaning,"Where is the center or the edge of our Universe?" ? Of course not, because the whole surface is the universe, nothing inside and nothing outside the sphere.
So the edge and the center of the Universe are everywhere and no-where at the same time. Because the Universe is the surface of a 3-sphere and there is no meaning of edge here.
I think the cosmos don't have a edge. If it does not have a edge it is oval in shape as there is no edge on a circle or an oval.