Primordial viscosity, diffusivity, Reynolds numbers, sound and turbulence in the beginnings of gravitational structure formation

The first structures were proto-voids formed in the primordial plasma when viscous forces balanced gravitational forces at the Hubble, or horizon, scale of causal connection LH ≡ ct ≈ LSV ≡ (γν/ρG) , where t ≈ 30 000 years was the age of the universe, c the speed of light, γ ≈ 1/t the rate of strain, ν the kinematic viscosity, and LSV Gibson’s 1996 viscous Schwarz scale. The photon viscosity ν ≈ 4 × 10 m s gives near-critical horizon-Reynolds-number ReH ≡ c t/ν ≈ 200, strong sonic damping, and fragmentation at a mass of 1016M⊙ to form proto-super-clusters. Before neutralization the expanding, cooling plasma continued its fragmentation to proto-galaxy masses with constant baryonic density ρ ≈ 10 kg m, suppressing turbulence formation by both buoyancy and viscous forces. This explains the observed δT/T ≈ 10 cosmic microwave background temperature fluctuations as a reflection of non-turbulent structures and not sound waves. After neutralization at t ≈ 300 000 years, simultaneous fragmentation occurred within each proto-galaxy at both Jeans and viscous Schwarz scales to form ≈ 10 proto-globular-star-clusters (PGCs, ρ ≈ 10 kg m), each comprising trillions of condensing small-planetary-mass primordial-fog-particles (PFPs). Dark PGC clumps of PFPs that have not yet accreted to form stars persist as the galactic dark matter, supporting Schild’s 1996 quasar-microlensing interpretation. Non-baryonic dark matter with D ≥ 10 m s diffused to fill the expanding proto-voids until fragmentation as galaxy-cluster-halos at diffusive Schwarz scales LSD ≡ (D /ρG). Subject headings: cosmology: theory — dark matter — Galaxy: halo — turbulence