The Hubble volume is the volume that corresponds to objects so far from the Earth that the space between us and them is expanding faster than the speed of light. (I.e. objects outside this volume could never again be visible to us, even in principle.)
The volume of the observable Universe extends from us to the maximum distance light could have travelled since the Universe became transparent; when It was roughly 380,000 years old.
Since c1998 we have known the expansion of the Universe is accelerating, implying that the number of galaxies within the Hubble volume is decreasing. Since the Big Bang (well infinitesimally close to it at least) we know that time has been going forwards, and thus that the observable Universe is expanding.
When do these two volumes coincide with one another and what will the corresponding maximum volume of the observable Universe be at that time? The associated calculation or link to a suitable reference would also be very much appreciated.
I have often wondered about this; ever since reading Professor Sir Roger Penrose's Cycle's of Time a year or two ago. I thought about it again today after reading a somewhat unassociated article about how recent results had shown the accelerating expansion of the Universe cannot be explained by the "Hubble Bubble" hypothesis. Before asking this question I did of course search the site for an existing answer: this question is extremely similar but does not appear to include an exact answer (in fact the answers appear to somewhat contradict each other. Moreover, it does not appear to address the subtleties involved in making the estimate; such as the variation in inter-galactic recession speeds, due to the change in gravitational force between them, since the Big Bang.