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I am struggling to reconcile the Hubble volume with the idea of a cosmic event horizon.

As I understand, the Hubble volume is increasing over time because Hubble's constant is decreasing. This should allow photons emitted in superluminal regions to enter into the Hubble volume and become subluminal.

The cosmic event horizon, as I understand it, is the point where any light emitted beyond the cosmic event horizon will never reach Earth.

So, can a galaxy emit light that can reach us, but then pass over the cosmic event horizon, such that any light it emits after this point will never reach us? And, if the Hubble volume is increasing in diameter, why can't it overtake the cosmic event horizon, allowing the light in this region to now travel subluminally?

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  • $\begingroup$ In particular about objects moving in and out horizons this or other materials from the same authors should be what you are looking for. arxiv.org/abs/astro-ph/0310808 $\endgroup$ – Alchimista May 9 at 9:51
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No, the Hubble sphere can never extend over the cosmic event horizon; it can only asymptotically approach it.

The Hubble sphere is the region within which galaxies (and other stuff) recede from us slower than light. The event horizon is the region outside which no light can ever reach us. If the Hubble sphere extended beyond the event horizon, it would mean that there exist a region in spacetime that recede subluminally, but which we could never see. But we have always been, and will always be, able to see light from subliminal regions.

However, a galaxy can cross the event horizon, such that it is no longer able to emit light that we can see. This is most easily seen in comoving coordinates, i.e. the coordinates that expand along with the Universe. In these coordinates, galaxies have fixed positions, but the event horizon is always shrinking.

In the spacetime diagram below you see time as a function of comoving coordinates. We are where the blue lines cross. The yellow region is the part of spacetime from which we may receive a signal, bounded by the event horizon (orange), and slowly approaching the Hubble sphere (purple). Galaxies at fixed coordinates follow lines parallel to the black dotted line, and may hence eventually cross the horizon.

For example, today the distance to the horizon is 16.5 Glyr. A galaxy at this distance may emit a photon now that we may detect in a almost infinitely distant future, redshifted to the extreme radio regime.

But tomorrow, it's too late.

spacetime

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  • $\begingroup$ Thank you very much for the explanation! It makes a lot of sense. So does the graph above assume an accelerating Universe because the Hubble Sphere is decreasing in radius? And at t=infinity, anything that isn't in our immediate proximity will pass the Hubble sphere and the cosmic event horizon? $\endgroup$ – Matthew May 12 at 17:27
  • $\begingroup$ Also, how do we determine where the Event Horizon is today? Is it the boundary where the galaxies are receding so fast that a photon emitted by one of the galaxies can never be overtaken by the Hubble sphere? $\endgroup$ – Matthew May 12 at 17:37
  • $\begingroup$ @Matthew Yes, a spacetime diagram is based on a set of cosmological parameters; here I used the Planck 2016 values where dark energy takes over around t ~ 10 Gyr, making the Hubble radius decrease. But remember that this is comoving coordinates; in physical coordinate it doesn't decrease, but asymptotically approaches ~17 Glyr, so not really "immediate proximity" (however, if the dark energy has an evolving eq. of state, this could change such that the Hubble sphere decreases to r→0, ripping apart galaxies, stars, planets, and eventually atoms in a Big Rip). $\endgroup$ – pela May 13 at 16:08
  • $\begingroup$ And yes, the Event Horizon separates the part of spacetime from which we may receive a signal, from the part where we can not. This also depends on cosmology; for instance, in a universe with no dark energy, there is no region that we won't eventually be able to see if we just wait long enough (in theory; in practice sufficiently distant galaxies will be too faint and too redshifted). $\endgroup$ – pela May 13 at 16:12
  • $\begingroup$ It is an interesting and often misunderstood fact that, at all times, the distance to the EH is larger than to the Hubble sphere (though they approach each other), meaning that there will alway be galaxies receding faster than the speed of light which may still be able to see. For instance, today d(EH) = 16.5 Glyr while d(Hub) = 14.4 Glyr. So all galaxies in the shell between 14.4 and 16.5 Glyr are currently receding FTL, but we may still one day see the light that they emit today. $\endgroup$ – pela May 13 at 16:17

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