What would we find if we could travel 786 trillion light years in any direction
I've sometimes heard of galaxies that are millions or billions of light years away but if we could instantly travel 786 trillion light years in any direction, what are we likely to find? And what if we continued on for another 786 trillion light years?
PS: I'm not a physicist.
I really find this question confusing because it doesn't explain why you picked that number. If it's arbitrary, you should say so.
I'm afraid the only correct answer to this question is that nobody knows.
Cosmology is based on a number of simplifying assumptions (sometimes called principles) - the most basic of which is that the universe is "isotropic and homogeneous on large scales". Isotropic means that is (or looks) the same in any direction; homogeneous means that what we see does not depend on our position in the universe.
This "cosmological principle" is reasonably well tested and would certainly make sense if the universe were very much bigger than we are capable of seeing. The most distant thing we can "see" in our universe is the cosmic microwave background (CMB), the light of which has been travelling for about 13.6 billion years. However, if we were to think about a parcel of gas that emitted the CMB and where it is now, we could calcuate that it is about 46 billion light years away due to the expansion of space in the universe. Thus the "edge of the observable universe" is about 46 billion light years.
What we can say, is that on these scales the Universe is very isotropic, and homogeneous, because the CMB is very smooth and looks the same in all directions to a very good approximation (but see below). This suggests that if you were to travel 46 billion light years in any direction, that you would probably have a very similar view to what we have now (that is, if you were able to miraculously travel instantaneously; if you travelled more slowly then of course the universe would continue to get older).
You are talking about travelling more than a factor 10000 further. On these scales we do not know anything outside of speculation. The inflationary model for the big bang might suggest that our observable universe is just a tiny part of a much greater entity and that within this very much larger entity everything will be homogeneous and isotropic at a given cosmic time. However, the recent very precise Planck measurements of the CMB, suggest there may be small, but real, anisotropies on scales as big as the observable universe, which would then suggest that any extrapolation by a factor of 10000 might be wishful thinking.
We would likely find galaxies. The universe, as far as we can observe, is very uniform on the large scale. Depending on the geometry of the universe, may be the place we left for travalling. For a fixed cosmic time the spacetime seems to be curved in a way that the universe looks finite when travelling along a straight (geodesic) line, although without boundary.
There is one principle that says "The universe is isotropic". It means it looks the same (on large scales) from any point you look from.
This means, in turn, that if you travel 786 trillion light years instantaneously in some direction, you'll find a very differnt sky but with exactly the same general structure: stars, galaxies, clusters of galaxies, and attractors.
Altough you can NOT travel so far so fast, you can make this mind experiment:
Send a spaceship so far at (almost) speed of light with a photo camera, take a 360º photo, come back, arrive 1572 triilion years afterwards.
While awaiting for the spaceship return, wait 786 trillion light years, take a 360º photo, wait the othe 768 trillion years.
Compare the two photos. They were taken at the same "Cosmic time", one of them 768 trillion years ago, here, and the other one maybe two or three years of spaceship time ago, 768 trillion light years afar.
The photos will look the the same on the rough scale.