Can the Hubble Sphere ever extend over the cosmic event horizon? 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?
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.