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tisdag 1 oktober 2024

Visible Matter vs Invisible/Dark Matter

The apparent gravitational presence of invisible/dark matter is a key open problem of modern cosmology. 

Recent posts seek an answer as Neo-Newtonian Cosmology NNC starting with a primordial gravitational potential \phi as a rapidly oscillating small amplitude perturbation of a zero potential from which mass density 

  • \rho\equiv\Delta\phi\ge 0 

is created through the action of the Laplacian differential operator \Delta acting in a Euclidean infinite space. 

We assume a decomposition \rho =\rho_v +\rho_{iv} with \rho_v as substantial and localised representing visible matter, and \rho_{iv} as small and distributed representing invisible/dark matter with clear separation. With u=u_v+u_{iv} as total matter velocity decomposed into velocity u_v of visible matter and u_{iv} that of invisible dark matter, NNC takes the following concise form:

  1. \rho_v+\rho_{iv} = \Delta\phi                           (inverse square gravitational law in differential form)
  2. \dot\rho_v =-\nabla\cdot (\rho_v u_v)                   (conservation of visible matter)
  3. \dot\rho_{iv} =-\nabla\cdot (\rho_{iv} u_{iv})                 (conservation of invisible/dark matter)
  4. \dot u_v=-\nabla\phi                                    (Newton's 2nd Law for visible matter) 
  5. \dot u_{iv}=-\nabla\phi                                  (Newton's 2nd Law for invisible/dark matter) 
We see that the total gravitational force -\nabla\phi acts on both visible matter and invisible/dark matter in qualitatively different ways, with precise motion of visible matter as high density + localised and imprecise motion of invisible/dark matter as low density + distributed. 

The observed velocity distribution of visible matter of spiral galaxies can now be understood as driven by gravitational force from \nabla\phi resulting from presence of high density localised visible matter together with presence of  low density distributed invisible/dark matter.

The key assumption is that visible matter as high density localised in the form of protons and electrons carries electromagnetics, while invisible/dark matter as low density distributed of unknown form, does not. 

Here high density localised represents stars and galaxies separated by large apparent voids, while low density distributed may represent a large halo around a galaxy, see below. 

It is natural to extend to dark energy as \Delta\phi <0 as small + distributed with an effect of anti-gravity or repulsion between matter of different sign (and attraction for same sign).

NNC naturally explains an expanding Universe from repulsion between matter of different sign.



Questions: 
  • Why does the dark matter halo not gravitationally contract? Is the density too small? Is the rate of contraction very small? Is it possible that the invisible/dark matter does not react to gravitational force, only contributes to gravitational potential? 
  • Is the visible galaxy formed from a primordial halo by gravitational contraction of in its center into visible matter? 

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