Creating the Universe by Plucking a String 1

Under the label New View on Gravitation I have tested the idea of letting gravitational potential $\phi (x,t)$ with $x$ a Euclidean coordinate and $t$ a time coordinate, have a primordial role from which mass density $\rho (x,t)$ is "created" by the Laplacian differential operator $\Delta$:

• $\rho (x,t) = \Delta \phi (x,t)$ for all $x$,         (G1)

assumed to act without time delay for all $t$. Mass is thus created locally for each $x$ by differentiation as an instant local operation acting at each time instant $t$.  

This is to be compared with the standard view that gravitational potential $\phi$  is created from primordial mass density as solution of the differential equation:

• $\Delta\phi (x,t)=\rho (x,t) $ for all $x$,           (G2)

represented by the integral formula

• $\phi (x,t) =-\frac{1}{4\pi}\int\frac{\rho (y,t)}{\vert x-y\vert}dy$

which requires instant action at distance and so represents a main mystery of modern physics.

We recall that the Laplacian is invariant under an orthogonal change of coordinates and so the creation process (G1) is independent of the choice of Euclidean coordinate system, which can be seen as a sign of possible physicality. 

(G1) allows "creation of something big from something small" in the following way: Let us start from a gravitational potential $\Phi =0$ satisfying $\Delta\Phi =0$ thus with corresponding zero mass density. Let $\Phi$ be subject to a small scale small amplitude oscillatory perturbation $\phi$ creating small scale large amplitude oscillatory mass density $\rho =\Delta\phi$ by the action of second order differentiation with $\rho =\rho_++\rho_-$ decomposed into positive mass density $\rho_+$ and negative mass density $\rho_-$.  

The action of gravitational force $-\nabla\phi$ will cause attraction between mass densities of the same sign and repulsion between mass densities of opposite sign, and so will segregate the small scale variation of $\rho$ into one Universe of positive mass and another of negative mass which repel each other and so recede. 

By the action of the Laplacian on a small scale small amplitude oscillating perturbation of a zero state gravitational potential $\Phi =0$, a large scale large amplitude positive Universe $U_+$ with positive mass $\rho_+$ has thus been created, which is balanced by a corresponding negative mass Universe $U_-$ at eventually large distance. 

It is thus possible to envision a scenario where a small perturbation of a zero gravitational potential by the action of differentiation + gravitational attraction/repulsion generates a large scale Universe with positive mass thus representing "creation of something very big from something very small".  

Does this mean that the scenario really starts from zero? Not quite, because starting from $\Phi =0$ satisfying $\Delta\Phi =0$ requires some spatial structure to express the Laplacian. We can see this spatial structure as a string under tension and the small scale small amplitude perturbation as a small amplitude high frequency excitation of the string. 

The creation process thus starts with a spatial structure under tension but without excitation, from which the Universe we are living in is created with "a little pluck of a string".

The scenario opens to the existence of dark matter identified by $\Delta\phi$ of small magnitude but large extension, and dark energy as influence on $U_+$ from $U_-$.