Distribution of Primes versus that of matter (LM and DM) for early universe; both non-uniform – mathematical and physical truth?
To expect the primes to be uniform in distribution would seem a just so idealization i.e. atypical. Randomness is just an idealization. One could also consider clustered primes in 3-dimensions, with still a non-uniform distribution, and compare it to non-uniform distribution of matter in early universe. Evenly distributed matter (DM and LM) for early universe would seem like a special condition, since non-uniform distribution (voids, proto-voids, and non-void clustering) for macro-scale would seem more typical. Thus physical models would seem to have to describe just evolution from such more typical early macro-stage, rather than assuming perfect uniformity (randomness) for such distribution. The latter being just an idealized assumption. One could compare to alternative scenarios (top-down, and bottom-up models, and clustering in general – but not enough time). However perhaps one has to accept early universe distribution of matter as like physical truth; not so unlike clustering of primes as mathematical truth? That is, was there no choice, as the curtain rises at the end of the Dark Age?
Elaborating: For ‘universe’ of ~13.8 Byrs (i.e. one manifold element of alleged set of manifolds, in SRM), one has recombination at ~370,000 years; and re-ionization at perhaps ~300-600 Myrs? Then the first stars and observed galaxies (from dwarf mergers?) appear to form very early. But there is not enough time for such formation. Also even if dark matter is considered as massive neutrinos, becoming non-relativistic at ~10,000 years after Big Bang and Big Expansion, still not enough time for any aggregation into galactic halos, nor for any Zeldovich like pancake super-structure, with super clusters and voids. Hence is 3-D clustering a more typical rendition for such early universe; not unlike the clustering of prime numbers, rather than an assumed idealized uniformity? Also might heterogeneity, rather than assumption of homogeneity, be more typical for nucleosynthesis stage, although results are the same? Also globular clusters form early (stellar age of ~12 byrs ago?). Might such globular clusters also have a strong infrared signature, consistent with copious still older red dwarfs? TMM
Cowen Ron, Galaxy formation: Cosmic dawn, Nature 497, p. 554-556, 30 May 2013, and references therein. [brief summation]
Bouwens, R. J. et al, Discovery of z~ 8 Galaxies in the HUDF from ultra-deep WFC3/IR Observations, http://arxiv.org/abs/0909.1803 (2009).