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.

Part 3 ... Mordechai Milgrom is a reputable careful worker

Mordechai Milgrom is a reputable careful worker. His data are used to support the idea of Dark Matter, not MOND. Not by him, though, he still teaches MOND. Where do we get Dark Matter from GR or from the standard theory of particle physics? Where?

WIMPS are even more hypothetical and unfalsifiable. DM itself is just a patch used to fill in the blanks in Friedmann. If one can derive Newton from GR, then one can derive the hyperbolic (1/kr) black-hole galactic gravitational field using the right assumptions. These would be interesting in themselves...

Unfalsifiable hypotheses cannot be used to refute facts. TeVeS theory is such an hypothesis like such quantum/GR hybrids all are. They have never predicted one single unique item and no such prediction has ever been verified. A theory that does not predict competently is not a theory and does not deserve the attention of mathematicians nor scientists.

All math, all science, is metaphor. All language is ultimately just metaphor including, and especially, Scripture. It is impossible to fully capture reality with any kind of human language. Prodessionals' neglect of this principle is what many people mean when they claim that scientists are insufferably arrogant and grossly naive. These critics go too far, though. Then they claim science is Myth. They create this Myth. Let us endeavor NOT to do so ourselves.


Gak

No cynic is happy.

Model for the Inflationary Growth of the Universe

PHENOMENOLOGICAL EQUATION
FOR THE EXPONENTIAL CONTRACTION
OR EXPANSION OF THE UNIVERSE

I do not believe that anyone has ever published an intuitive equation that purports to graphically describe, extensively (not intensively), the expansion of the universe according to the current standard model from near the beginning of time to the present and beyond. By means of a system of Edisonian trial and error guided by theory, boundary conditions and empirical evidence, I have produced such an equation. I consider it to be semi-theoretical but with strong empirical input from observation of the phenomenon. Eventually, I hope, It will be derived from first principles.

I started with Allan Guth’s concept of initial exponential inflationary expansion followed by Hubble’s idea of more moderate expansion beyond this preparatory process. By varying parameters, deceleration, constant expansion or acceleration in the modern era can be reproduced as well as initial exponential inflationary expansion. Guthian inflation, according to these equations, has a few twists, as we shall see.

I use Einstein’s natural units because no other basis will allow exponentials of the type that I employ to work. Therefore, the current "radius" or radius of the light horizon of the universe, the speed of light and the current age of the universe are all set equal to 1. Equation 3 is an idealized representation of Guth’s exponential inflation. It depends on the "relativistic" time form given in equation 1 which contains the parameter e.

To force the equation to describe deceleration in the present era, a value above about e=100 should be chosen. To produce an equation that describes acceleration in the present era, a value of rather lower than e=100 should be chosen. The values of A and B are chosen to make the equation conform to empirical boundary conditions, including the fact that the exponential expansion curve should always pass through the points (0,0) and (1,1).

In other words, once the boundary conditions are satisfied, e controls only the curvature.

See the next post for two tables of the equations I used with their variables and parameters. Sorry, the equations are written in single line format, that is, using nested parentheses, (() ), ^ for exponentiation, etc.