Nuclear synthesis occurs for over 90 seconds, or 10² in comparison to Planck time of 10^-43 seconds, thus seemingly 45 orders far removed from r_m modified global radius minimum of modified global trajectory and of 3-volume minimum. Still 31 orders from Electro-weak energy scale of ~10^-12 seconds to Planck scale? Nevertheless cosmic time i.e. large scale peculiar velocity, Hubble parameter (changing 3-volume), and fermion mass spectrum are all exponentially changing, in SRM Spiral Rotation Model; thus shortening cosmic time duration to high entropy transition stage of r_m. The latter an entropic caldera of quanta interactions and extreme manifold deformations i.e. sea of gravity waves? Is this the ‘world’ we came from; forged in a cosmic crucible?

## June 8, 2016

## April 7, 2014

### Planck scale revealed at extremely early r_m minimum stage of 3-manifold trajectory?

Might Planck finer scale also be descriptive for rm minimum modified global radius stage for 3-manifold i.e. for 3-volume in SRM Spiral Rotation Model; that is, at earliest transition stage of Big Bang i.e. Big Expansion? For such extremely early transient stage, might there be a sea of gravity waves; thus revealing a description of the Planck scale for all stages? In SRM, one entertains the simplifying assumption that one always has mass and curvature description for all equiangular spiral stages of 3-manifold’s cyclical trajectory; hence always a greater than Planck scale. Conservatively then perhaps ~4 orders of magnitude (~10-29 cm.?) greater than Planck scale? Is this then the smaller scale 3-volume ‘world’ that we came from?

For extremely transient very early stage, one allegedly would have extreme deformations of 3-manifold. Yet tangent vector, and hence differentiation, geodesics, in addition to mass and curvature, are still allegedly descriptive. However no alleged change of topology for such stage, nor for any stage. That is, no handles, nor multi-connectedness, nor patches of manifold missing. Also geodesics allegedly never end; rather no longer defined on still finer Planck scale.

Such extreme curvature of manifold allegedly is associated with resistance to such deformations i.e. so-called inertia of manifold. The latter allegedly being a special case of the greater generality: as if manifolds want to be left unperturbed; that is, if disjoint or intersecting, then always so. So resistance to deformation, and no topological change i.e. no handles, no change in connectedness, no loss of, nor sudden mixing, of elements of sets – that is, no change in continuity.

However such extreme deformations, and resistance to deformations, is herein considered associated with copious quanta creation from physical vacuum; thus contributing to stress tensor and thus to further extremes of deformations i.e. extreme curvature. Would this seem consistent with fermion mass spectrum , exponentially increasing in mass and number of generations, increasingly shorter transitions; that is, a maximizing of entropy in comparison to alternative scenarios? Thus consistent with the adage ‘anything not forbidden, will occur’? TMM

Weirstrauss function: continuous, but nowhere differential. Like for finer than Planck scale?

## December 17, 2012

### Mathematical truth and physical truth?

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).