Primordial viscosity, diffusivity, Reynolds numbers, sound and turbulence at the onset of gravitational structure formation

The first structures were proto-voids formed in the primordial plasma when viscous and weak turbulence forces balanced gravitational forces at the scale of causal connection LH ≡ ct ≈ LSV ≡ (γν/ρG) 1/2 ≈ LST ≡ ε /(ρG) at time t ≈ 30 000 years (10 s) the age of the universe, with c the speed of light, γ ≈ 1/t the rate of strain, ν the kinematic viscosity, and LSV and LST Gibson’s 1996 viscous and turbulent Schwarz scales. The photon viscosity ν ≈ 4 × 10 m s suggests weak turbulence from the Reynolds number ReH ≡ c t/ν ≈ 200, and fragmentation at ρL3SV ≈ 10 16M⊙ to give proto-super-clusters, buoyancy forces, fossil turbulence, and strong sonic damping. The expanding, cooling plasma continued fragmentation to proto-galaxy-mass ≈ 1012M⊙ with ρ ≈ 10 −17 kg m and γ ≈ 10 s preserved as fossils of the first turbulence. Turbulence fossilization and gravitational instability explains the small δT/T ≈ 10 cosmic microwave background temperature fluctuations as evidence of earlier structure formation rather than sound waves. After plasma to gas transition at t ≈ 300 000 years (10 s), gas fragmentation occurred within each proto-galaxy at both LJ ≈ 10 4LSV and LSV ≈ LST scales to form ≈ 10 11 proto-globular-star-clusters (PGCs), each comprising ≈ 10 small-planetary-mass primordial-fog-particles (PFPs). Dark PGC clumps of PFPs, not yet accreted to form stars, persist as inner-galaxy-halo dark matter, supporting Schild’s 1996 quasar-microlensing interpretation. Non-baryonic dark matter, with D ≥ 10 m s, diffused into expanding proto-voids and fragmented as outer-galaxy-halos at diffusive Schwarz scales LSD ≡ (D /ρG), indicating light, weakly-collisional, fluid particles. Subject headings: cosmology: theory — dark matter — Galaxy: halo — turbulence