Hi Georgina
I apologise for the slow reply. I would like to have prepared this explanation for you while having more time on my hands, however I guess I better make a start.
I will present a couple of analogies that are somewhat comparable to my cosmological model. The general idea that we are testing, is that matter is dependent upon an interaction with space, that is the source of the energy that motivates atomic forces. So conceptually this is a very simple and intuitive consideration, and the analogies I give will reflex this simplicity. Analogies that serve this consideration are, the relationship between a candle flame and atmospheric oxygen, that the intensity of the flame is dependent on atmospheric oxygen density. Another analogy might be, an electrical appliance circuited with a battery, and the relationship between battery capacitance and an appliances ability to undertake energetic work.
I think the first step in realizing this might be a worthwhile use of your time, would be based on the prospect of assigning fundamental forces with a prior cause. It can be surmised that fundamental forces undertake work actions in the world, and so long as fundamental forces remain theoretically causeless, then this ability to undertake work also remains causeless. Is "causeless work" a reasonable notion to ascribe too?
My hypothesis is that the observations and measures which indicate to us that space has an expansive property, corresponds to a regenerative elemental field of space. I refer to the observation and measure of cosmological redshift, which is one and the same thing as the cosmological constant, and Dark Energy. That this continually emergent field is a universal energy supply, which matter is dependent upon to drive its fundamental force. So we will begin with three main parameters to quantifying a system of this type, then expand it to a forth parameter. We begin with 1. volume, 2. energy density throughout that volume 3. Intensity of an entity which is dependent upon that energy source. Then we incorporate the forth parameter which is, replenishment rate of that energy source.
We have a perfectly sealed room of set volume, which contains an oxygen density, and we place a candle within the room, its flame intensity dependent on oxygen availability. We set a clock ticking. Obviously the room volume remains a constant, so it is the oxygen density and flame intensity which is a declining variable parameter over time. It is also worth noting that oxygen density and flame intensity will share proportionality with one another during their mutual decline. Let us suppose that after 10 hours the room is nearly depleted of oxygen and the candle is about to wink out.
Now place two candles with the same room and set the clock ticking. Room volume and oxygen density remain the same parameters as the first experiment, but now the parameter of flame intensity is doubled. By doubling the demand on the oxygen supply, the rooms oxygen density and therefore flame intensity, decrease at twice the rate of the previous experiment. Adding further candles to the room, the results are simple arithmetic.
Forth parameter
A slightly more dynamic circumstance would be if the oxygen supply within the room was steadily replenished. Perhaps leaking under the door. Let us consider the example whereby there is one candle placed in the room, and the oxygen replenishment was set at precisely the same rate as the candles rate of oxygen consumption. All four considered parameters would remain constant over time, in balance with one another. The room volume, oxygen density, oxygen replenishment rate, and flame intensity.
Now we place two candles within the room, with the oxygen replenishment rate set as before mentioned, enough to replace the oxygen demand of one candle only. What happens? The system as a whole is not in equilibrium, so the oxygen density in the room and flame intensity will decline proportionately with one another until equilibrium is re-established. Equilibrium will be restored when each candle burns at half original intensity, which added together equals, the rate of oxygen replenishment. This relationship is important for my hypothesis, that between the replenishment rate of oxygen and flame intensity. Please take its note.
So what am I all about? What am I alluding too? If the cosmological constant corresponds to the replenishment rate of an elemental field, which is the source of atomic force via an interaction between space and matter, then the same general parameters will apply, and you would expect appropriate values to demonstrate correlation. Paul Dirac's Large Numbers Hypothesis deals with precisely these parameters. Auv conforming to replenishment rate, his measures of distance serve as components of universal volume and density of matter distributed within that volume, and then he determines (there exists an equality between the measure of Auv which we relate to replenishment rate, and a measure that corresponds to value of atomic force).
We can verify this by analysing Paul Dirac's 9 minute video in explanation of the Large Numbers Hypothesis. We simply list the parameters he mentions and this becomes clear.
So there is a good deal more to discuss, but none of it is overly complex and or unintuitive. Every point I make can be related back to simple considerations of simple analogous systems. But I want to quickly jump to the end game, where I am leading you, so you are not in the dark in this respect.
The end game hypothesis is this.
If Gluon activity "which is the primary giver of mass" is a variable value, dependent and proportional to energy density of space, in the same general way candle flame intensity is dependent on oxygen density. Then we can infer a relationship of proportionality between the density distribution of matter in galaxies, and a variable gluon activity, which is variable baryon mass. Gluon activity will directly correlate to universal matter densities.
Here's the evidence this works.
By studying galaxy luminosity profiles, it has been deduced that star densities within spiral galaxies generally decline by square of the distance from galaxy centre. That is the same thing as saying, matter densities decline by this uniformed value. If we now relate the proportionality of gluon activity and star density as before mentioned, it can be hypothesized. Gluon activity increases by square of distance from galaxy centre, in lock step as star density declines by square of the distance. Gluon activity equating to mass, then this places mass in precisely the correct place, and precisely the correct value to correct galaxy rotation curves. A variable baryon mass hypothesis, with an exacting mathematical formula, based on volume of space, Auv energy density within volume of space, and predicted Tuv gluon activity.
Based on a theory that provides an answer to the universal measures we have taken and the unexplained equality they are known to demonstrate. By ascribing atomic forces to a prior cause, which also describes a universal system that continually regenerates and can conceptually compound changes over time, evolve, develop intricate complexities through the only natural process we are aware of capable of achieving such articulated order, Darwinian. Give nature a natural energy potential and it will invent a circumstance of Darwinian emergence. The observations and measures that lead to Dark Energies inference, could point to just such a natural potential, from which complex universal systems have arisen.
The measures taken that define the Dark Matter puzzle couldn't fit this hypothesis any better than they do. A mathematical relation between volume of space and Gluon activity. Hopefully I will be afforded the opportunity to explain these considerations here at FQXi.
I jumped right ahead here, but backing up a bit. What do you think of my oxygen filled room and candle flame analogy. Do you have any questions about it?
Thanks for listening Georgina.
Kind regards
Steve