This is a case of an unwisely chosen simile taken waaaay too far. This idea, that the entire universe could be inside the event horizon of not a supermassive, but rather a superduperultrahypermegastupendouslymassive black hole, is usually introduced in introductory classes about general relativity. The instructor in this case is trying to make clear that, contrary to a fairly popular misconception, the event horizon of a black hole is locally flat. That is, there are no CGI-fireworks, nor any kind of hard "surface", nor anything else particularly special, in the immediate vicinity of the event horizon. The only special thing that happens is a long distance effect, like noticing that every direction now points off in the distance towards the singularity.
The simile is also used to point out that, at the event horizon, even second-order, nearly local effects (that is, curvature of spacetime, or tidal effects in other words) become less pronounced the more massive the black hole is. (As an aside, this also explains why Hawking radiation is more intense for smaller black holes) So... as the simile suggests, if the black hole were massive enough, we might not even be able to detect it.
The key, though is massive enough. First of all, the whole beauty of the Einstein curvature tensor (the left side of Einstein's equation) is that it is Lorentz invariant, so it can be calculated in any reference frame, including one that is hypothetically based inside an event horizon.
The curvature can still be unambiguously calculated, so when you suggest that it may be only an optical illusion, you are also suggesting that all the scientists who do that type of large-scale curvature calculation (not me personally) are totally incompetent. Just so you know. I would suggest not mentioning that at any conferences on cosmology. One of the enduring mysteries of modern cosmology is that the large-scale curvature of the Universe seems to be open (like the 3-space-plus-one-time dimensional analog of a saddle or Pringle potato chip) and not flat (like Euclidean geometry) or closed (like a sphere). The last is what we would calculate if the visible Universe were inside a black hole.
So, for the visible Universe to be inside an event horizon, the Cosmic Acceleration we have seen thus far would have to actually just be one small, contrarian region inside an even larger event horizon of globally closed curvature. Just to make the event horizon radius 13.7 giga-lightyears (a bare minimum starting point that excludes all manner of things that make the real situation many orders of magnitude worse*), you would need over 8E52 kg of mass in the singularity. This would require over 5E79 protons, where I have heard that the entire visible Universe only has about 10^80 particles, total, and I think I heard that there are about 10^18 photons for every proton, or maybe even all other particles. Somebody can look that up if they want to, but it's definitely a big number. The upshot is that there would have to be an amount of mass, all crammed into one singularity, that would render the total mass of every single thing we can see a barely detectable rounding error. Monkeying with all those dark matter and even dark energy theories is less of a leap than that.
Your prediction doesn't actually predict anything, since you account for either its presence or its absence.
Speculation 1: Olber's Paradox is already solved for accepted theories of cosmology, so pointing out that your theory can also resolve it is nice but doesn't score any points.
Speculation 2: Are you suggesting that the singularity is where all the antimatter to match the Universe's matter went? Remember the singularity dwarfs the visible Universe. That still doesn't explain the asymmetry, it only pushes the question back by one logical step: Why did the antimatter go into the big singularity and not the matter?
Speculation 3: Hawking radiation for the big singularity's event horizon lends whole new meaning to the term negligible. See my previous aside. Also, we can't observe matter being destroyed at the singularity. That's information flowing the wrong way. Also, that negates the previous assertion that the sky is black because it's towards the singularity.
*Like cosmic expansion, just how small our contrarian region is, compared to the whole event horizon, and probably some other, subtler things.
Let's start with some general notions. The Cosmological Principle postulates that at each location in the universe one can define a hypothetical observer to whom the universe appears isotropic and homogeneous. Such observers are called comoving observers, and we can define a comoving coordinate system, in which these observers remain at rest; this means that comoving coordinates are expanding along with the universe. Which each comoving observer, we can also associate a cosmological time.
With this in mind, we can introduce two types of distance:
The proper distance $D_\text{p}$ is the distance between two regions of space at a constant cosmological time. As the universe expands, the proper distance between two comoving observers increases over time. This notion of distance is purely theoretical, because we cannot see where an object is 'right now'. After all, it took time for light to travel from the object to us, during which the universe expanded. But given a cosmological model, we can derive the proper distance of an object from observations.
The comoving distance $D_\text{c}$ is a distance in expressed in comoving coordinates. By definition, the comoving distance between two comoving regions of space remains fixed at all times. It is related to the proper distance as follows:
$$D_\text{p}(t) = a(t)\,D_\text{c},$$
where the function $a(t)$ is the scale factor, which describes the expansion of space as a function of time. At the Big Bang $a=0$, and by convention at the current cosmological time $a=1$. In other words, at the present day both notions of distance coincide.
The change in proper distance over time between two comoving regions of space is called the recession velocity $v$, and we get
$$
v(t) = \dot{a}(t)\,D_\text{c} = H(t)\,D_\text{p}(t),
$$
where we introduced the Hubble parameter $H(t) = \dot{a}/a$. This is the famous Hubble Law.
Let's now examine the expansion of the universe in more detail. The three graphs below are spacetime diagrams of the Standard Model of Cosmology (the $\Lambda$CDM model) according to the latest data:
Distances are given in Gigalightyears (bottom axes) and Gigaparsec (top axes). Cosmological times are shown on the left vertical axes, and the corresponding scale factors are shown on the right vertical axes.
The 1st graph depicts proper distance as a function of time, and the 2nd depicts comoving distance as a function of time. The 3rd graph is essentially the same as the second, but the time axis is rescaled in such a way that light rays are moving on straight lines at $45^\circ$ angles.
The black vertical line in the middle is our own world line (or more precisely, the world line of a comoving observer at our location). The horizontal black line indicates the current cosmological time (13.8 billion years after the Big Bang). So, we are currently located at the intersection of these two lines.
The world lines of a number of comoving regions of space are represented by dotted lines. In terms of proper distance (1st graph) these lines are diverging as space expands. In terms of comoving distance (2nd and 3rd graphs) these regions are at rest, so their world lines are vertical.
The green curve is the Hubble radius. Regions of space inside it (green area) have recession velocities smaller than $c$, regions outside have recession velocities bigger than $c$.
All right, time to address your questions.
If I understand correctly, it means the most distant object that we can see right now is 46.5 Gyl away (at present),
There were no stars or galaxies in the very early universe, so 'the most distant region of space' is a better term. But otherwise yes, that's correct.
but it was 13.7 Gly away at 13.7 billion years ago.
No, it was much closer to us (and theoretically it was $0$ at the Big Bang). Remember that the universe expanded between the time that the photons were emitted and the present day, increasing the distance that photons had to travel to us. Those photons had to overcome the expansion of space in order to reach us, so they must have started much closer than 13.7 Gly from us.
The paths of those photons correspond with the orange curve; it marks the edge of our line cone. So all the photons that we currently observe have travelled on this path, and this is the cross-section of the universe that we actually observe right now. As light rays travelled to us, they travelled through different comoving regions, which I've indicated by a number of grey dots.
Notice that at early times the photons moved through regions outside the Hubble radius. This meant that their proper distance to us was actually increasing at early times, since the speed of the photons wasn't able to compete with the recession velocity of the region of space in which they were moving. Nevertheless, over time they moved through regions with smaller recession velocities, and eventually they did cross the Hubble radius (this happened when the universe was ~4.4 billion years old). From then on, their proper distance decreased, until they finally reach us today.
In theory, the oldest light that we can observe would've been emitted right after the Big Bang ($t\approx 0$). The world line of the corresponding region of space is the lightmagenta dashed line. The current proper distance of that region is ~46.5 Gly (the magenta dot on the horizontal black line) and it is the present-day edge of our observable universe. At every cosmological time, we have a different light cone and a different corresponding region that marks the edge. If we plot this edge at each cosmological time we obtain the particle horizon (blue curve). Notice that it actually corresponds with the path of a photon that started at our location at $t=0$. Which means that an observer that the current edge of our observable universe is 'right now' receiving light emitted from our location at $t=0$
This contradicts my understanding, based on which the expansion accounts for a 239% increase in the radius of the observable universe! Where is the misinterpretation?
You misunderstood the paragraph. It talks about the difference between the theoretical edge of our observable universe and how far we're actually able to see in practice. The reason is that the very early universe was so dense that it was opaque to light. It wasn't until the universe was about 400,000 years old that light decoupled from matter and the universe became transparent. That moment, called the epoch of recombination, is the oldest light that we can see, and we see it as the cosmic microwave background. This edge of the visible universe has a current distance of ~45.5 Gly, which is about 2% smaller than the theoretical edge of the observable universe.
It means the observable universe will be 62 Gly at some point in the future. How can the observable universe become larger if its edge is expanding faster than light?
As I explained earlier, some photons can travel through regions with recession velocities larger than $c$ and still reach us, as long as they cross the Hubble radius at some point. But as you can see from the graphs, photons emitted at $t=0$ beyond a comoving distance of ~62 Gly are never going to cross the Hubble radius (the world line of this region is the darkmagenta dashed curve). They're too far away to overcome the expansion of space, so they can never reach us. The edge beyond which photons cannot reach us is called the cosmic event horizon (red curve). It's also the edge of our light cone at $t=\infty$.
I hope this helps, it's a lot to digest. Some further reading:
Comoving and proper distances
Hubble's law
Cosmic microwave background
A more technical but very enlightening paper:
Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe
Some of my own, more technical posts on this subject:
What is the theoretical limit for farthest we can see back in time and distance?
Does space expansion imply light will never reach objects currently distant enough?
Can space expand with unlimited speed?
Best Answer
In standard cosmology, the answer to the bolded question is "yes", while the answer to the second one is "no".
There is a way to define an absolute reference frame, in that any observer can measure the dipole moment of CMB radiation and determine the velocity with which they are moving through it (see section 2.1 in this Planck paper, for example).
What this means is that the universe is not invariant with respect to Lorentz boosts, but it is (at large enough scales) invariant with respect to rotations and shifts, so there is no center or preferential direction to speak of.
The existence of this "preferential" frame does not invalidate the general principle of relativity --- physics can be described in other frames just as well if we do a coordinate transformation. However, this particular one is interesting in that we can unambiguously refer to it from anywhere in the universe.