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Firstly, regarding the observable universe there is a certain radius of a circle, and we cannot see further than that. It is understandable, that due to photons travelling at a certain speed we can only see that far. But question is: "What happens with photons that might arrive later to our vision?", meaning outside our "ring" of the observable universe, to my understanding we could detect also photons or radiation coming from there, meaning that our radius of the visible universe is expanding, in the sense of areas now, where we can have layers of certain visibility and with a percentage of "accuracy" and not a static radius, i.e. "x light years beyond the radius the existence of one y object has been confirmed due to late photons coming to our vision. There might or might not be more around it but we have no certainty". Understanding human life is too short to experience that change, these humans might be living some thousands of years from now. Until here I have considered a static model, I haven't taken into account universe expansion yet.

When the universe expansion speed is put into the equation, things change. If the universe expansion is faster than the speed of light, we would be "losing ground" in visibility, meaning more objects would be leaving our radius than the ones coming, however nothing is faster than the speed of light, meaning that the universe expansion is smaller than speed of light (unconfirmed quotation), thus in reality to me, our vision should be expanding, but slower than the static model I described a little earlier.

On the other hand, at the edge of our imaginary ring, we can also have objects popping in and out from time to time. In this manner we can also create an uncertain map of what was and what will be in the outer ring of our observable universe, thus expanding our vision, and over time this map will be more certain.

Now, I haven't done the math, nor am I certain of many of my quotations, so please don't be angry at me, I am just a curious human being trying to learn more about our universe :)

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Unfortunately, the limit of the observable universe isn't just "photons from the big bang arriving to us now" - so we won't see anything past it because nothing existed before; anything outside that sphere didn't arrive yet. This limit is called the Hubble Sphere, and is only the "first stage" of unobservability - and indeed, as time passes what we can see will expand and we'll be able to see further.

But there's another limit - called the cosmic event horizon - which, to current knowledge, is quite unconquerable. It's connected with space expansion. Space expansion is a phenomenon of far objects "moving" further apart, with the nasty property of bypassing special relativity with its property of light speed being the same in all frames of reference (which would normally imply no matter how far a light source, the light would reach us sooner or later). Instead of classic motion - change of position in space over time - the "motion" due to space expansion is "production of more space" between the objects - they aren't actually in motion relative to each other (or that motion is irrelevant), it's the very definition of distance between them that is changed.

And as result of that, there is a region distant enough, that light from there - traveling at speed of light towards us - will never reach us as there will be always more space inserted between it and us, per unit of time, than it can cover. And so, the cosmic event horizon describes the actual ultimate sphere of the observable universe, not just "for now" but "forever, unless we discover some way to bypass it, but currently not even a hint of such bypass exists."

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    $\begingroup$ Good answer, but one minor thing: The Hubble Sphere is defined as the region within which the Universe expands slower than light. This region is well within the observable Universe; in fact galaxies at the “edge” of the Hubble Sphere are only at redshift $z\sim1.5$. What you describe in the beginning is called the Particle Horizon, and matter there is at redshift $z\rightarrow\infty$, and recedes at $v\simeq3.3c$. $\endgroup$ – pela Oct 26 '20 at 22:03

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