Chronos said:
I still am struggling to reconcile all this with, for example, this article
https://www.relativitycalculator.com/articles/the_end_of_cosmology/the_end_of_cosmology.html, where it is noted in the illustration on p48 "at the onset of acceleration we see the largest number of galaxies that we ever will".
I've spent some hours now banging my head against the wall trying to understand what Krauss and Scherrer meant by that statement.
Here's what I managed to figure out, hopefully it makes some sense:
First, in the oft-cited
Davis & Lineweaver paper an equivalent statement by Krauss is quoted as an example of 'misconceptions or easily misinterpreted statements in literature':
[13] Krauss, L. M. and Starkman, G. D. 1999, ApJ, 531(1), 22–30, Life, the universe and nothing: Life and death in an ever-expanding universe, “Equating this recession velocity to the speed of light c, one finds the physical distance to the so-called de Sitter horizon... This horizon, is a sphere enclosing a region, outside of which no new information can reach the observer at the center”. This would be true if only applied to empty universes with a cosmological constant - de Sitter universes. However this is not its usage: “the universe became Λ-dominated at about 1/2 its present age. The ‘in principle’ observable region of the Universe has been shrinking ever since. ... Objects more distant than the de Sitter horizon [Hubble Sphere] now will forever remain unobservable.”
Notice the objection by D&L.
This gave me some hope that I'm not entirely misguided in my understanding.
It is, however, unclear whether D&L think the statement is an example of misconception or just an easy to misinterpret one. Taken on the face value it would have to be the former as Hubble sphere is an even horizon only in empty (no matter), lambda-dominated universes, or in the infinite future of universes with matter (such as ours). But I'd give the professional cosmologists who wrote that some more credit.
The original paper available on arxiv provides some context:
Krauss, L. M. and Starkman, G. D., Life, the universe and nothing: Life and death in an ever-expanding universe
In the light of then-recent discoveries of dark energy driving the expansion, the authors estimate that in our universe observable objects beyond our local supercluster will become redshifted beyond detectability (wavelengths longer than the horizon diameter) in a finite time.
They acknowledge that the de-Sitter horizon is not strictly applicable to our universe, but argue that it will become practically equivalent to the actual event horizon in relatively short time.
Since the event horizon in time becomes equivalent to the Hubble sphere, the ability of the observers in the far future to see non-locally bound galaxies can be estimated based on whether or not galaxies stay within the Hubble sphere as the universe evolves.
If we now look at the spacetime graph:
we can see that at the moment of beginning of acceleration (thin horizontal red line) there was the maximum number of galaxies lying within the Hubble sphere (vertical red line - each of the comoving distance vertical lines we may draw on the graph, starting at the origin, is equivalent to the worldlines of consecutively farther galaxies).
Up to that point, galaxies were crossing the Hubble sphere from the 'outside'. From that point on, they are crossing it from the inside.
This fact in itself doesn't mean anything - again, the Hubble sphere is not a horizon in our universe, so the mere fact that a galaxy or an older (e.g. CMBR) signal crosses it doesn't make it unobservable.
However, the point in time where Hubble sphere begins shrinking in comoving distance terms marks a change in the 'fates' of the observability of galaxies in the far future.
It's not a real change, though, since the observability of a signal emitted at any comoving distance is uniquely determined in a given model. It can be seen just by looking at the curve of the actual event horizon - if it's outside, it'll never be observed, if it's within, it'll always be casually connected (even if redshifted beyond detectability).
I see this as a more of a 'what if' scenario: what if the slope of the curve of the Hubble sphere could be held constant at say 5 Gy? Then the far-future observers would see more and more galaxies, forever, no problem. What if it could be held constant at the point of switch from deceleration to acceleration? Then they'd see the amount of galaxies contained within for all time, while the more distant ones (and CMBR) get redshifted beyond observability. What if the curve keeps evolving like it does? They'll be stuck with their local supercluster only.
We're in the latter scenario, so the best possible 'chance' for the future observers to be in a non-desolate universe already passed.
At least that's the best I could come up with. Maybe there's a better reason for using that picture by Krauss, Scherrer and Starkman. Maybe in the popular article it's just a convenient picture to paint the process of galaxies 'escaping', maybe in the paper it's just a shorthand used to make rough estimates. Maybe something else. Far for me to say that I understand the topic better than the authors of either publication.
