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This paper by Toby Ord states this: "There is substantial confusion about how to interpret the Hubble volume, with widespread erroneous claims that we could never affect (or see) galaxies beyond this limit.19 In fact, this radius is about 14.4 billion light years and is smaller than the affectable universe. We can thus affect some of the galaxies beyond the Hubble volume. This may at first sound impossible, since these galaxies are receding at a speed greater than that of light. But the explanation lies in the fact that proper velocities of the things we send after them (including light) also grow as they get further away from us (for the space between us expands) so these can exceed the speed of light too, and sometimes catch up. This will even happen in practice, for if you have ever shone a light into the sky, some of the photons released will eventually reach the edge of the affectable universe, and thus beyond the Hubble volume. By symmetry, some light from galaxies beyond the Hubble volume will eventually reach the Earth."

In his paper, the affectable universe (which he states cosmologists call the "event horizon") is a sphere with a 16.5 billion light-year radius (so slightly larger than the 14.4 billion light-year radius Hubble volume).

https://arxiv.org/pdf/2104.01191.pdf

Either I'm completely misunderstanding, or his description doesn't seem correct at all. IIRC, the 16 bly event horizon is merely the region outside of which no light will ever reach us, and the reason why it is slightly larger than the Hubble volume is because the Hubble volume is increasing. This means that photons emitted by galaxies in a superluminal region inside of the cosmological event horizon can eventually enter inside of our Hubble sphere and be able to reach us. If the Hubble constant wasn't decreasing, the event horizon and the Hubble volume would be one and the same.

The reasoning outlined by Ord about being able to affect galaxies outside of the Hubble volume doesn't make sense to me. Sure, light will recede faster from Earth the more distance it covers due to expansion, but any object outside of the Hubble volume is already moving away at a rate that exceeds the speed of light and will also recede faster the further it goes. There's no way to close the distance. The space between any photon fired from Earth and any object beyond that horizon will only increase, causing the object beyond that horizon to move even faster away from the photon.

The reason why light emitted from a galaxy beyond the Hubble volume can reach us is not because that light is "catching up" - it is receding, but its rate of recession doesn't outpace the growth of our Hubble volume.

Am I simply misunderstanding?

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    $\begingroup$ Ord is right. If you look at the spacetime diagram linked to by PM 2Ring you’ll see that light, moving at 45°, is able to cross the Hubble sphere. For instance, the vertical dashed line shows the worldline of galaxy GN-z11, which is seen to never have been inside the Hubble sphere; yet we see it. $\endgroup$
    – pela
    Commented Oct 13, 2022 at 20:29
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    $\begingroup$ I don’t know why someone has downvoted you though; it’s a good question that many get wrong (including e.g. Neil deGrasse Tyson). $\endgroup$
    – pela
    Commented Oct 13, 2022 at 20:30
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    $\begingroup$ @pela Oh I want someone to roast Tyson about that so bad! He's so good at roasting others (e.g. the stars in Titanic (1997)) Is there some particular video, paper or article you can link to? $\endgroup$
    – uhoh
    Commented Oct 14, 2022 at 0:19
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    $\begingroup$ @pela Thanks for the reply, maybe I wasn't clear as to my question though - I agree we can receive light from objects inside our event horizon, but would this hold if our Hubble sphere wasn't expanding? I have no doubt that Ord is right about us being able to receive light from outside our Hubble sphere, but I don't understand his explanation. The way in which he phrases it makes it sound like light in superluminally receding regions of space can "close the distance" and catch up to us, while as I understand it the reason why is because of the expansion of our Hubble sphere. $\endgroup$ Commented Oct 14, 2022 at 0:20
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    $\begingroup$ the-protean: I don't think it's right to say that the reason is that the Hubble sphere expands, because the reason for this is the accelerated expansion. Light crossing the Hubble sphere would happen also for non-accelerated expansion, which is exactly what the ant-on-a-rubber-rope puzzle is about. $\endgroup$
    – pela
    Commented Oct 15, 2022 at 18:02

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The symmetry that Ord invokes is just the homogeneity+isotropy of FLRW cosmologies. If light from a distant object can eventually reach us, then, swapping the roles of emitter and receiver, light we emit at the same cosmological time can eventually reach it.

The recession speed between light we emit and an object farther than the Hubble distance is initially positive, but can become negative as the Hubble distance increases. This is the same argument you used to (correctly) argue that the light from the distant objects can reach us.

As far as physical understanding goes, I wouldn't put too much stock in this kind of argument, since it's largely an artifact of the coordinates used. As a specific example, the $ρ=p=Λ=0$ expanding FLRW cosmology is just flat Minkowski space in different coordinates, and the Hubble sphere is, in Minkowski coordinates, a sphere expanding at the speed $c\tanh 1\approx 0.76c$. Obviously there is no difficulty in communicating bidirectionally across this surface. The reason that light emitted from this surface toward the center is momentarily "at rest" relative to the center in FLRW coordinates is just that the FLRW distances are measured along curved lines whose radius of curvature varies with time. In general FLRW cosmologies it remains true that FLRW distance is not a very good measure of geometric distance; it's similar to measuring distances on Earth along lines of constant latitude instead of great circles. The recession speed, being based on FLRW distance, is not a very good measure of relative speed either.

Because of that, I wouldn't worry too much about which description (Ord's, Davis & Lineweaver's, etc.) is more correct. They are probably all mathematically correct, and none of them is a good way to get physical intuition. It's better to think in coordinate-free terms of a spacetime manifold and geodesics on it and no particular decomposition into "space" and "time", and treat the coordinate arguments as calculational conveniences.

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