Newton vs Big Bang, Dark Energy and Dark Matter

In her latest post Sabine Hossenfelder asks if we can get energy for free e g in the form of Dark Energy as a main mystery of modern cosmology. Let us see what Newton can bring to this question starting with his law of gravitation: 

• $\Delta\phi =\rho$ or $\rho =\Delta\phi$          

connecting mass density $\rho (x,t)$ to gravitational potential $\phi (x,t)$ though the Laplacian differential operator $\Delta$ with $x$ a Euclidean space coordinate and $t$ time. 

The standard view is that mass density is non-negative $\rho (x,t)\ge 0$ for all $(x,t)$, but if we expand the scope why not allow $\rho (x,t)$ to also locally be negative, then corresponding to some form of negative mass. If we dare to take this step, we find the following remarkable facts:

1. With $\rho (x,t)$ an initial vanishingly small perturbation of an initial zero state varying very quickly in space between positive and negative values, the corresponding potential $\phi (x,t)$ will inflate to substantial size, as if gravitational potential is created out of nothing. This may correspond to a Big Bang from which a Universe filled with both positive and negative mass can evolve. 
2. Regions with negative mass density repel regions with positive mass density and so create an expansion seemingly out of nothing, which may correspond to Dark Energy, while larger regions of small positive and negative mass density can form and then locally contract by gravitational attraction into galaxies with large local density.
3. Large regions where $\phi (x,t)$ is slowly varying with $\rho (x,t)=\Delta\phi (x,t)\ge 0$ small may correspond to Dark Matter, which is not visible but still has major gravitational effect.     

In one shot, we thus open to new views on both Big Bang, Dark Energy and Dark Matter. Any comment?

More substance to such a scenario is given in blog posts on New Newtonian Cosmology.