Suppose there is a discrepancy from the time sub atomic particles gained mass and the initial rate of inflation. If there was, for a mere fraction of a second, a period of super density before inflation kicked, in could that provide a sufficient density of matter to grow massive black holes of this size that subverts the above mentions limit?
It didn't start as a single singularity - it started as many, in a matter-dense region of space in the early universe - possibly primordial singularities, or first generation super-massive stellar formed singularities, in a cluster.
If these each then accrete matter from the space surrounding them, they do so independently and each can accrue mass faster than a single singularity of equivalent total mass could while adhering to the Eddington limit. Once the space surrounding them ends up mostly devoid of other matter, the only remaining gravitational influence on them is each other, and thus they start to fall together, coalescing and increasing in mass, changing spin and vector, and potentially causing further coalescence and the availability of fresh matter to consume.
Ultimately, this process would result in a single supermassive singularity which would be exceedingly hot, as it would be massive enough to take in matter from a much larger area than its ancestors, and would do so at a vast rate due to the matter previously being relatively untouched.
Anyway, that's my armchair physicist hypothesis.
The Eddington limit is a linear function of mass, so the accretion onto a collection of objects would not differ from the accretion onto a single object. At least, not because of the Eddington limit – (hydro)dynamics would play a role.
> Ultimately, this process would result in a single supermassive singularity which would be exceedingly hot, as it would be massive enough to take in matter from a much larger area than its ancestors, and would do so at a vast rate due to the matter previously being relatively untouched.
I'm not sure what object you are referring to as "hot". The accretion disks around black holes typically become _cooler_, as the black hole mass increases. And, black holes themselves are aqutally quite cold, as they do not emit significant amounts of radiation.
Black holes can not merge - time dilation means it would take an infinite amount of time for them to do so.
1. The bottom-up model: After the first generation of star formation, the most massive stars formed black holes with masses somewhere between 10-100 solar masses. These then began accreting material and merging with each other and gradually grew into the supermassive black holes we see today.
2. The direct collapse model: As galaxies were forming, there was generally a concentration of gas at the bottom of each galaxy's potential well. If this cloud were dense enough, under the right conditions it could collapse directly into a ~10^4-10^6 solar mass black hole without fragmenting into individual stars.
The bottom-up model has historically been considered more plausible because the physics involved is better understood. However, discoveries of very massive black holes very early in the lifetime of the universe are starting to pose very serious challenges for this model. The reason is that black holes cannot grow arbitrarily rapidly. The rate at which a black hole can accrete matter is limited by the "Eddington accretion rate" or the "Eddington limit." Above the Eddington limit the gas gets so hot as it accretes onto the black hole that radiation from the infalling gas blows away the rest of the gas. (There are many details in this process which I have glossed over, but suffice to say it's generally difficult to get an accretion rate that is much more than this limit.)
If you start out with a black hole with a mass of ~100 solar masses and you feed it constantly at the Eddington limit, you can just barely grow black holes large enough to power the quasars we see in the early universe. But as more distant and more massive black holes are discovered, it gets harder and harder to grow a stellar mass black hole into a supermassive black hole in the age that the universe has existed at that time, and you have to invoke mechanisms like super-Eddington accretion and black hole mergers to grow a large enough black hole. This may be possible for individual black holes, but the more fine-tuned the model becomes, the less likely it is to be the primary channel by which supermassive black holes form. These sorts of discoveries are therefore providing evidence that the simple bottom-up picture may not be correct and either super-Eddington accretion, mergers, or direct collapse is necessary to form these black holes.