We can only see as far as light has been able to travel in 14 billion years. Since light travels at a finite speed, we can’t see what’s, say, 100 billion light years away, because if there’s anything out there, the light from it hasn’t reached us yet.
According to our best current theory, space expanded much, much faster than the speed of light for a fraction of a second during the Big Bang, and has continued to expand at a slower but measurable rate since then. This is how light from the very first stars and galaxies can be hitting out telescopes now, but it also means that in the 14 billion years their light has been going through space, space has expanded more – so those stars are more than 14 billion light-years away.
Thus, the farthest (& oldest) things we can see are now about 46 billion light years away from us, in any direction. This is the size of the *observable universe*. This distance is always growing, at the speed of light – in one year, light emitted from one light-year farther away at the start of the universe will have had time to reach Earth. We estimate that there’s maybe several hundred billion galaxies in the observable universe.
It’s reasonable to assume that there’s more stuff beyond that, since it’s not a real boundary in space. Whether it goes forever, or “stops” somewhere, or if 3D space is “curved” and you’d eventually end up “looping back around” like going around a globe, these are all hypotheses, but I don’t know how we’d ever get evidence to actually narrow it down to one answer.
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