There is no boundary to the Universe-as-we-theorize-it.
The boundary to the Universe-as-we-observe-it is a sphere of radius 47 Gly. This is the proper distance, i.e., between where we are, and where those objects are now. The age of the universe is 13.8 Ga, which is the time taken for that light to reach us. (Actually less time, because the light that reaches us -- redshifted to the CMB -- was emitted at about 0.1 Ga.)
The early universe apparently expanded extremely rapidly, hence we can see things which, at the time, were within our light-cone (of 13.8 Gly radius), but have since expanded beyond our horizon.
The property of expansion (or shrinking, or asymptotic quiescence inbetween those cases) is an inherent result of the Friedmann–Lemaître–Robertson–Walker metric. Namely: if you initialize space with a uniform distribution of matter, and set time moving, you get a universe that naturally expands (or not), all on its own. And, as a result of that, an observer, at a point, sees distant matter passing out of their horizon (or in from it).
Based on this theory, we can reasonably suppose that the Universe-as-we-theorize-it is truly infinite. Or at least, several times larger than the ~50Gly we know about.
The only restriction is observational, practical: we cannot see beyond our horizon, because at some distance through a uniformly expanding universe, the relative motion exceeds the speed of light. (There's nothing wrong with that: space-time can do what it pleases. The expansion isn't driven by internal energy, but space-time doesn't need to be conservative either.) So, there's little to no point talking about matter that's >100 Gly away from us; there's no possibility that we can interact with it, or vice versa.
Earlier estimates of universe expansion suggested it was slowing, at enough of a rate to eventually collapse. This showed up in pop culture
from time to time. While that would be an amusing fate, elegant even; modern data suggests it's
pretty damned close to flat, like cosmic-coincidence-of-coincidences flat. The asymptote will be zero density, but it will take a very long time indeed to get there (like 10^20 years). At that time, all energy will be red-shifted to a very cold CMB, and all matter will have collapsed into black holes, or evaporated into energy and red-shifted away.
Of course, this is a continuing subject of research, so although our existing error bounds are quite good (like the age of the universe), they concern a fairly narrow history; the wider and more subtle dynamics, that we can't resolve right now (like how early expansion was so fast, and how our fate will ultimately play out), are wide open, only speculation right now.
Tim
Home
Help
Search
Login
Register
