New Newtonian Cosmology: Universe from Nothing

New Newtonian Cosmology Magics

In recent posts I have tested the idea that mass of density $\rho (x)$ is "assigned" to matter through a gravitational potential $\phi (x)$ by $\rho (x)=\Delta\phi (x)$, where $\Delta$ is the Laplacian differential operator with respect to a Euclidean space coordinate $x$. The gravitational potential $\phi (x)$ also generates a gravitational acceleration $-\nabla\phi (x)$ acting on matter, where $\nabla$ is the gradient with respect to $x$, with $-\rho (x)\nabla\phi (x)$ the corresponding gravitational force density. I refer to this as New Newtonian Cosmology.

The idea is that mass density can arise from a small oscillation $\phi (x)$  of a zero ground state of the gravitational potential "creating" by differentiation an amplified oscillating mass density of variable sign with repulsion between matter of positive and negative mass densities into separated domains or Universa with positive and negative mass density. 

Focussing on a Universe with positive mass density $\rho (x)=\Delta\phi (x)$, we can see it arising form amplification of a small oscillating perturbation $\phi (x)$ of a zero gravitational potential. If we take into account the extremely small average mass density of the visible Universe (around 8 protons per $m^3$), we see that an even smaller original perturbation $\phi (x)$ would have been enough. 

It is thus possible to see a primordial Universe with very small evenly distributed matter/mass being created from a very small perturbation of a gravitational potential. In a next step of formation gravitation would then concentrate distributed matter into galaxies and stars, supplied with kinetic and heat/nuclear energy balanced by a decrease of gravitational potential energy. 

New Newtonian Cosmology thus offers a creation process without the massive input of energy required in a Big Bang. The key steps of "creation from nothing" are

1. Extremely small distributed positive mass density from an even smaller gravitational potential perturbation combined with gravitational separation from negative mass density.
2. Extremely strong concentration of positive mass density by gravitational collapse. 

This process can be complemented with a partially analogous process of generation of positive and negative charge from a perturbation of an electric potential supported by energy from gravitational collapse. 

In the previous post we observed that the "nothing" is not really nothing since we start with a zero state $\Phi =0$ of the equation $\Delta\Phi =0$ assuming the existence of Euclidean space.  

You can play with this model in Leibniz World of Mathematics Model Workshop under 21. Cosmology.