Joseph de Nicola said:
Imagine that in the same way a star with enough mass eventually collapses into a black hole, that it would take the combined mass of all the black holes in this universe to collapse into a new big bang.
This is not supported by mainstream physics. At best there may be a few highly theoretical models which make vague predictions concerning this, but in no way is this a well supported idea. One problematic thing that comes to mind is that this says nothing about all the matter and energy not locked up in black holes. All that gas, dust, and radiation roaming about contributes an awful lot to the mass of the universe. Another thing is that we don't even know how many black holes there are in the observable portion of the universe, let alone the rest of the universe.
Joseph de Nicola said:
But the black holes are constantly merging. The SMBH at the center of our Milky way can be thought of as a member of a binary black hole, with its partner being the SMBH at the center of Andromeda. In around 4.5 billion years they will merge.
Unlikely. The SMBH at the center of our universe is smaller in size than our solar system. The chances of another black hole of comparable size getting close enough to it to merge is
extremely remote. Even if they enter into a closer orbit around their barycenter, the time it would take for gravitational radiation to bleed off enough energy for their orbits to carry them close enough to merge might be longer than the time it takes them to evaporate via hawking radiation.
Joseph de Nicola said:
Perhaps at a certain point, enough SMBHs will accumulate to create such a strong gravitational force that it begins to reverse the effects of the inflationary period that began with big bang. You see where this is going. Imagine the entire universe eventually condensed into one huge black hole mass, with a few stray atoms some light years away, waiting for those last few bits of mass to join it to achieve critical mass, where that black hole collapses into a singularity and then bounces into a new bang.
I assume you're talking about something similar to the 'big bounce' scenario, where the universe reverses its expansion and collapses in on itself, only to rebound at a certain point. If so, you should know that black holes have nothing to do with this beyond contributing their normal mass. Just like regular matter and dark matter.
Joseph de Nicola said:
Also, there is enough good mathematics supporting various multiverse scenarios that I don't think one can assume that this or any universe is infinite.
On the contrary, the idea that the universe is infinite in size is very well supported by math, while multiverse theories have only the vaguest mathematical treatment. Basically, there isn't enough good math to support any multiverse theory over any of the others, let alone over a single-universe theory (aka the standard model of cosmology). Going beyond the math, there isn't a shred of evidence from observations or experiments supporting multiverse theories over the standard model of cosmology at this time.
Joseph de Nicola said:
Space is curved, therefore, one of the three proposed models of the universe's shape, positive curvature, would dictate that the universe is spherical, a very large bubble that only looks flat to us in the same way the Earth seems flat while we are walking on it - because it's so vast.
It's possible, but there have been no measurements made to date that have found any deviation from a flat shape. Note that the shape of the universe and the curvature of space as usually talked about in GR are related, but not the same thing. Space can be curved locally while the universe can be flat. An analogy (and only an analogy) is to think of a large sheet of thin metal with a hammer divot in the middle of it. Locally, the surface of the metal might be heavily curved near the divot. But the overall shape is still a flat sheet. Unfortunately it is very difficult to go from a 2d analogy to the 4d model, so don't expect everything to make perfect sense without a serious amount of time and effort spent learning the details of GR and cosmology.