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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