(September 8, 2016 at 11:15 pm)Alex K Wrote:Thank you for all this! Obviously I have a lot of work ahead of me.
Ok I can't sleep so I can just as well answer.
Dude that may all sound completely compelling to you, but you can't construct a serious cosmological or particle physics model with a bunch of words and a few numbers thrown in. It may sound superficially like that's what people did, but that's not how it works. When you say I have a new geometry, where are the differential geometry calculations outlining it, or the group theory? A geometry of what exactly anyway? The many other words you use - if they have a clear scientific or mathematical definition, it is only known to yourself. How does your "star tetrahedron" describe or govern the field? Which field? How does it describe the field and how does this field square with the known symmetries of the standard model? Are you proposing a new discrete symmetry? If so is it quantitatively compatible with known particle masses and interactions? That's 10 pages of calculations right there.
One can propose geometric symmetries (so called flavor symmetries) on the fermions, but then you have to specify the group representations of all known fields, and how they are broken by some dynamical mechanism to yield the observed masses and quark and lepton mixing parameters. That's 10 pages of calculations without which you don't have a model. The problem is that you can vaguely throw together an infinite number of schemes which are all wrong. Only when it quantitatively fits with known physics in all detail does one have anything.
For instance, Gell-Mann and Zweig and all the others working on this in the 60s and later didn't just say, look, the number 8 looks promising, let's make it 8. They said, ok if we formally introduce three quarks (and the 8 fold way only employs the lightest 3, u d s, not the rest because they are to heavy for the scheme to work), they will exhibit a SU(3)xSU(3)xU(1)xU(1) partially conserved symmetry structure, and from the mathematical representations of these symmetry groups and the symmetry breaking, they could predict the light mesons and baryons, and calculate some of their masses. One of the structures appearing there is the adjoint representation of SU3 which happens to have 8 elements, but there are others with 6 or 10 etc... It's not a fundamental model though, just an old incomplete albeit very useful effective description of the bound states of the lightest three quarks. What I write here alone though is meaningless without the hundreds of pages of calculations establishing quantitatively what it all means.
To have a serious model for cosmic inflation, you need to specify the fields driving it and their dynamics and the analytic form of its potential from which you can derive parameters such as the spectral parameter and scalar to tensor, and then if you wish to address matter creation, a reheating process and numerical studies how baryon asymmetry is generated. This is a loooot of work.

"Leave it to me to find a way to be,
Consider me a satellite forever orbiting,
I knew the rules but the rules did not know me, guaranteed." - Eddie Vedder
Consider me a satellite forever orbiting,
I knew the rules but the rules did not know me, guaranteed." - Eddie Vedder