Size of Visible Universe: Why now ~50Bly instead of 15?

Question

I understand, I think, the argument that the position is based on. Said in a sentence, the 15Bly's is in the temporal dimension only therefore space drops out because the redshifting absorbs the interim expansion of space which maintains a constant $c$ throughout. When the measurement is not in terms of time but in terms of distance the redshifted component of light must be translated back to distance and added to the initial displacement.

I get the reasoning to the extent my explanation says I do (it might be wrong and if so please treat it as the first part of my question). I accept that the reasoning itself is self-consistent and that the conclusion reflects a legitimate way to look at things.

But despite trying quite hard, I haven't yet been able to see that this view merits its advancement from supplementary/alternative view to the primary view, displacing the observable physicality in the process. Let me briefly provide a little illustration.

Currently the number given to what is explicitly described as the observable or visible universe is ~50 Bly. As it is stated surely it is a false statement, for the physicality of what we see in the telescope, across the board is the universe as if no interim expansion ever happened.

This issue is not whether a larger universe can be anticipated, but whether the interim expansion merits being moved over from the unobservable-but-anticipated universe into the actual visible universe.

Surely that is a mistake, since the interim expansion is no more visible than any other region in the unobservable universe. It's not in our light cone.

So can anyone explain what is going on for me? It doesn't appear legitimate to cite redshift as the physical justification, because for one thing it has been known since Maxwell that redshift and time are mutually small 'r' relativistic. When we look at a high redshift galaxy, time is slower in the observed galaxy relative to the observer time from the perspective of the observer. That's surely the primary physicality, and not the view that adds the interim expansion. Not because the expanding universe is not the best explanation but because the interim expansion is outside our light cone.

Answer 1

Don't get confused, I know it can be, but if looked at carefully it's not that difficult. There are also great references to read or study.

The size of the observable universe is (approx) 93 billion light years (Gly). That's the diameter of it, and the radius 46.5 Gly. It is the comoving distance now to the objects we can see now (assuming no absorption and perfect detectors). We see the light that was emitted about 13.7 Gy ago, it took that long to get here, and because of the universe expansion the sources are now 46.5 Gly away. Observable universe is a very accurate name.

It's explained at Wikipedia at https://en.m.wikipedia.org/wiki/Observable_universe

This is also called the particle horizon, because it is the Largest distance from which something that happened in the universe at any time in the past could possibly have affected us, it is our causal horizon. That is, it is the observable universe, the part of the universe from which any signal could be reaching now or have reached us in the past.

There are other distance measures and horizons. That cited above is the comoving distance, now, to the emission of the light. If you wanted to know the distance then, when it was emitted, well, it was really 0, at around the Big Bang. However, a better distance measure then is had by getting the distance then to the microwave cosmic background radiation (CMB), which was let loose at about recombination time about 380 Ky after the Big Bang. The redshift to that is a little over 1000 (see one of the Wikipedia articles), and the distance then (at that time) to our (cosmologically extrapolated) position then is approx. the 46 Gly divided by redshift (or multiplied by the scale factor then, approx 1/z), so about 46/1000 = 46 Mly. That was outer approx distance from the so called surface of last scattering (when the light decoupled from electrons and was thus let loose)

A different horizon is the event horizon, which is the furthest away, in comoving distance, to a source that emits light now, and which we could possibly see in the future (i.e., could possibly reach us after traveling to us). See the Wikipedia article below, it turns out it's about 16 Gly away, and it would take 5 Gy to see that light.

https://en.m.wikipedia.org/wiki/List_of_cosmological_horizons

The latter, the event horizon, is the anticipated horizon. Light which leaves now from further away we will never see. The particle horizon is the limits of the light we do see now, 46.5 GLy, and which was emitted about 13.7-13.8 Gy

The best explanation and mathematical descriptions, along with great graphics of the different horizons and distances is in an article from 2003 (there must be something more recent, this may be slightly off on some of the cosmology parameters that have since been measured more accurately, but they are close enough for what you need, and the best, more explained and graphed results). See it at https://arxiv.org/abs/astro-ph/0310808

By the way, the 15 Gly, or more accurately 13.7 to 13.8 Gly is the so called Hubble distance, or the distance that light would travel during the age of the universe, if there was no expansion. It's in the articles also.

Answer 2

The maximum distance light has traveled is around 50 GLy even though it has only been 15 Gy since the big bang. The reason for the discrepancy is the expansion of the Universe. The light travels farther as it is traveling in an expanding space.