What would the size of the observable universe be if you traveled 3/4 the speed of light? I have a conceptual mess in my head and would like to clean it up.
From the perspective of Earth, we can measure the observable universe diameter at current at 93BLY.  I understand this and why/how that is done.  But, it seems that if I got in to a spaceship and left Earth and the immediate area, and increased my speed to, say, 80% the speed of light, then I measured the size of the observable universe from that perspective, I would measure a much smaller observable universe. (Traveling 80% speed of light is purely hypothetical, of course).
I tried to research this much, but cannot find any help to explain why or why not this may happen, leading me to believe that my question is moronic.  So, if anyone can explain the answer to my question, or why the question is in err, that would be great.
My brain says that if I [could] travel at [near] speed of light, my measurements would show a much smaller universe ahead of me, and no universe behind me, too!  Help.
 A: Length contraction in special relativity is something that happens when you set up a network of Einstein-synchronized clocks and metersticks, and make measurements when the clocks all show the same time.
The contracted length isn't what you measure if you're moving at a certain speed; it is, rather, what you measure if you use those clocks and metersticks to do the measurement. Introductions to special relativity often assume implicitly that for every person in the universe, at every time, there is an infinite network of clocks and metersticks that are at rest relative to that person, and that person uses those clocks and metersticks for all measurements and not the many others that are apparently also floating around.
In general relativity, it's not even possible in principle to set up Einstein-synchronized clocks at relative rest over a region large enough that spacetime curvature is significant, and the whole universe is obviously such a region.
If you were moving at a high speed (relative to local galaxies) through the universe, you would have the same length and time standards available for measurement as we do, and you would probably end up using the same cosmological coordinates that we do as a result, even though you happen to be moving at a high speed in those coordinates. (We are, in fact, moving at about $600\text{ km/s}$ relative to the cosmological coordinates that we use.)
That's not to say that you won't reach distant points in the universe faster than you'd calculate by naively dividing the distance by $v$. You will. It's just easier to attribute that to time dilation relative to the well defined cosmological coordinates, rather than length contraction relative to a coordinate system that can't obviously be defined at all.
A: If you know how is the distance measured, then you also know it is measured with respect to special inertial observers called comoving.
Special theory of relativity tells us, that no inertial frame of reference has priority a-priori. But some inertial reference frames do have priority if you introduce more structure. For example if you introduce heavy body, then the inertial frame which is at rest with this heavy body becomes preffered.
Similarly, when we introduce cosmological model, it picks special inertial frame of reference and in this frame we do our work. This frame is independent of the observer and is determined purely from structure of our cosmological model, in this case by symmetries of our cosmological model.
So even if you would travel at 80% speed of light relative to Earth, you would still be doing your cosmology research in comoving frame and not in your own and you would determined the same size.
That being said, you can work in your own frame, find out another number, but such number is of smaller use and is thus not used by cosmologists.
