New Newtonian Gravity Including Dark Matter

This is a continuation of previous posts on the gravitational potential $\phi (x)$ as primordial giving mass density $\rho (x)$ to matter by differentiation as instant local action 

• $\rho (x) =\Delta\phi (x)$      (1)

where $\Delta$ is the Laplacian differential operator with respect to a 3d space coordinate $x$. It is assumed that $\rho (x)$ is non-negative expressing absence of negative mass density. 

This is a non-standard view to be compared with the standard view with mass density primordial from which the gravitational potential is created as solution to the differential equation $\Delta\phi =\rho$ which is a global summation process appearing as instant action at distance. 

Both views, referred to as classical Newtonian gravity and new Newtoninan gravity formally express Newtonian gravity but they represent different physics. The big seemingly insurmountable problem of oldNewton since the days of Newton, is the physics of instant action at distance, which does not appear in newNewton. 

Further, newNewton opens to a distinction between visible matter and invisible matter or dark matter, through the smoothness or $\phi(x)$ that is the size of $\Delta\phi (x)\ge 0$:

1. $\phi (x)$ produces visible matter where $\Delta\phi (x)$ is large.
2. $\phi (x)$ produces invisible dark matter where $\Delta\phi (x)$ is small-moderate.     

You find here an very instructive discussion of the experimental evidence of dark matter including the following graph of mass distribution over a flat galaxy cluster with spotted high peaks of visible matter rising over a background of invisible dark matter (with clear separation): 

Notice that the total mass of the dark matter as present everywhere can be much larger than visible matter with pointed presence. 

I have argued that Newtonian gravity may represent a priori knowledge about the World which leaves Einsteinian gravity without role, with new Newtonian gravity in a natural way including dark energy.