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).