I think it will take us a long time to map the entire “surface” of the visible sphere. Eventually, telescopes will be able to pick up some of the farthest galaxies, but there will always be one which might be a bit farther away, even if it won’t be orders of magnitude farther.
The expansion of the universe is accelerating. At some point, the number of galaxies in the visible universe will stop growing and the light received from distant galaxies will grow more and more redshifted. However, it's possible that the redshifting will accelerate faster than our technological ability to detect more and more redshifted light.
I think we can fight back against this to some extent. The most distant galaxies are fading due to increasing redshift. If we build larger and larger radio telescopes then we should be able to continue seeing them at longer wavelengths. If in a billion years we manage to colonize a substantial chunk of our galaxy then maybe we could build a gigantic radio telescope out of many small collectors spread out over several light years.
The universe is likely infinite. The part we can observe is finite, and growing smaller.
Outside of our observable universe is probably just more universe. We're stuck in a bubble within that universe due to the speed of light and cosmic expansion. The expansion of the universe is accelerating and that expansion continually pushes more of the universe outside of our local bubble. Relative to our reference point, some parts of the universe are moving away faster than the speed of light.
Supposing you had some sort of mechanism to travel across the entire universe, when you get to what we on Earth would see as the 'edge' of the observable universe, you could see past the boundary to another section of the universe as big as this one. If you could communicate back to earth, you'd effectively increase the size of our observable universe by half.
But while we're still trapped by the speed of light, we can never see beyond the edge of the universe. An edge which grows closer and closer, faster and faster with every passing second.
No matter how big your sensor is, you can't detect photons that don't exist. Once an object passes beyond the boundary of our observable universe, it effectively ceases to exist for us. No photon from that object will ever reach us again.
There may be other cool tricks that we haven't thought of too. No reason that we need to make things bigger and colonize the galaxy if we figure out something neat that is smaller instead! eg: Maybe we figure out that we can accelerate small telescopes to some significant fraction of the speed of light for an observation. Or perhaps we find some other neat physical phenomena to manipulate incoming light.
The cool thing about scientific and engineering progress is that we can't know what we will discover and develop. 200 years ago, we started having electric lamps. In just 100 years time, we have gone from computers being fringe and folly to them being integrated into places they don't even need to be for sheer convenience. Assuming humanity makes it another 100 years and continues to advance technologically, things we only dream of today could easily be so common-place that people can't imagine living in the current dark-ages of technology.
Also, 100 years is a cosmic blip! If we are thinking ahead to the point where we can't see things in the universe that we can see today, humanity itself will likely not be recognizable from our current vantage point... assuming it exists at all.
Based on today a knowledge of the universe, even if humans colonize the entire universe, you would eventually lose contact with humans in certain areas and therefore their knowledge.
I felt like humans were doomed after watching it, despite the vast scales discussed.
Nothing in the universe can travel faster than the speed of light (we think), but the universe can expand faster than the speed of light. There are probably already objects we can't see and at some point in the far far future we will only be able to see objects in our own galaxy no matter how good our telescopes become.
When I learned that the universe is not constantly expanding/compressing with multiple big bang restarts, I was kind of saddened at the fact it's not. Not sure why, but I liked that idea. Maybe the never endingness about it?? The coldness of everything eventually being so far apart and all stars will eventually burn out and just be a dark place is just meh for an ending. Much more anti-climatic that way
Not everyone says the universe comes to a final end. Hindus and Buddhists believe in cycles, and Abrahamic religions believe in eternal heaven. Even scientists wouldn't all say that the universe conclusively comes to an end. It's one religion of many. You don't have to believe that one!
