Part 2 Try Alan Guth's "inflaton" particle

But, as far as other unfalsifiable new hypothetical heavy bosons are concerned - try Alan Guth's "inflaton" particle: A hyper-massive excited particle in a humongously excited "inflaton field" that cannot be distinguished from gravity itself, except by its degree of excitation.

Suddenly, it decays. It decays into daughter particles and these then decay. Some of this decay debris has a long half-life. And enormous mass. The rest decays into matter and energy as we know it. But, the long half life particles remain as ultra-massive black holes. These decay, not via Hawking radiation, but by virtue of their intense infinitely deep singular gravitational fields that cause them to erupt into this same universe (somewhere "else").

They spew out smaller black holes and matter/energy detritus like a Roman candle, (The Big Barf). Because of dependence on random processes and/or temperature, the daughter black holes they generate this way should follow a "normal" or "Poisson" distribution, perhaps. Statistically, this might be verified. Yet, it would take time for these BHs to start gathering in more matter to form full fledged galaxies. Some additional BHs may then form by accretion in the expected way.

Perhaps this process would indeed result in very ancient super-massive BH masses following a Poisson distribution. If I was a mathematical physicist, I am sure I could derive it. But, I am just a modeler.

Note that this process will result in sufficient inhomogeneity without invoking acoustic anomalies, quantum instabilities or other forms of additional turbulence to give the energy/mass distribution we see today, especially in the CMB.

Now for Black-Hole existence: the singularity case of a mass with radius r = 0 is different, however. If one asks that the solution set to the simultaneous homogeneous nonlinear partial differential equations in GR be valid for all r, one runs into a true physical singularity, or gravitational singularity, at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant (which says) at r = 0 the curvature blows up (becomes infinite) indicating the presence of a singularity. At this point, the metric, and space-time itself, is no longer well-defined, but not undefined.

For a long time it was thought that such a solution was non-physical. However, a greater understanding of general relativity led to the realization that such singularities were a generic feature of the GR theory and not just an exotic special case. Such solutions are now believed to exist and are termed black-holes. Because they certainly are gravitational singularities, they must have a unique gravitational potential field profile. By simple geometry, they must be distinguished by a hyperbolic (1/r) fall off in the gravitational field strength. This fact is currently being ignored.

F = GMm/kr, k = 1m (S.I., for dimensional integrity) means black-hole gravity falls off hyperbolically, not parabolically as according to Newton. This F equation is fully Newtonian, however. It just focuses on black-holes as being unique, and, of course, they are. Note that k = 1m is an explicit reminder that we deal with a gravitational singularity here.