Is it possible to explain by energy conservation the apparent expansion of the Universe with galaxies

seemingly repelling each other, as a compensation for the potential energy lost in the formation of galaxies by gravitational implosion? In short: Local implosion balanced by global explosion. Let us explore this natural and simple idea.

Let us thus as a basic cosmological model consider the *Euler equations* including gravitational forces expressing conservation of *mass*, *momentum* and *total energy* of gas in three-dimensional space over time.

We thus seek the *density* , *momentum* with the *velocity, heat (internal) energy* and *gravitational potential* as functions of space-time coordinates , where are space coordinates and is the velocity in the -direction. The Euler equations for read:

- ,

where is the partial derivative with respect to , is the partial derivative with respect to time , is the pressure and the gravitational constant. Further, denotes the divergence of , is the gradient and the Laplacian. We here leave the gas law defining the pressure in terms of the conservation variables to be determined.

We imagine that the gas in an initial rest state with uniform density and temperature is subject to a velocity perturbation which triggers a redistribution of matter into a set of galaxies with high density formed by gravitational attraction/implosion separated by voids of low density. This is an unstable process in the sense that perturbations of the gravitational potential are amplified into concentration-thinning of the density by the differentiation, with feed-back to the gravitational potential.

In the formation of a galaxy, the gravitational potential energy is decreased as matter is falling towards the center of the galaxy, and conservation of total energy requires compensating energy as increased internal energy of the galaxy and/or kinetic energy in the form of

- increased velocity inside galaxies
- increased velocities of whole galaxies.

Here 2. could be experienced as repulsion between galaxies. Loss of gravitational energy by implosion would thus be compensated by increase of kinetic energy of galaxies by repulsion expressed by the pressure , which would be determined by a gas law keeping the mean value of the net force small to allow the kinetic energy to reach a steady state. The repulsive force could be the force of dark energy. This comects to the view of George Chapline, who considers general relativity to be bogus along with black holes and instead supports an idea of dark-energy star.

The gas law would thus act to conserve the total energy, and may be compared with the gas law of incompressible gas acting to maintain incompressibility.

Notice that after the formation of galaxies the repulsive force would be shut off followed by inertial expansion as explored in Accelerating Expansion without Dark Energy?

Notice further that this model does not require any Big Bang, which is difficult to motivate, since the initial state is an innocent uniform rest state with uniform distribution of density and temperature. The Universe is then set in motion and formed through the instability inherent in the second order differentiation of the Laplacian.

## Michele

It seems to me (I’m quoting from memory) that the pressure power is div(pu). Is there any reason needing the pressure gradient is neglected?

I think that the “velocity perturbation” must be very strong. In this case would be due to a simple pressure wave?

Michele