Revised, 9/25/00

Exponentially Damped Spherical Bessel Function Wave Model of the Big Bang



Theory or Fit?

Is the Big Wave Model matter-deposition plot, which is postulated in the present work, the result of theory, or is it simply a fit to the NS galactic pencil survey data taken in the deep-red-shift surveys? If what you mean by the word theory is that the curve is derived from first principles, then the answer is no. We really don't know the details of what was going on inside the small or infinitesimal volume that existed just before the universe was created, so we don't know which equations to solve to produce the answer. In all cases regarding the Heisenberg Uncertainty Principle, we only know what went in and what came out, and we know that the conservation laws have been obeyed. But we are not privileged to see the internal details of the interaction.

However, the situation is not much better for the Cosmological Model of the Big Bang, where there are plentiful theories that really don't do very well to explain the observed structure in the universe. Theorists keep hoping that new experimental data will bail them out by providing something to confirm some of the many assumptions that have been made in order to make the existing theory work at all.

This is why the recent discovery of Cosmic Microwave Background fluctuations was greeted by cosmological theorists with so much enthusiasm! These fluctuations were needed to give the current model any hope of producing the ordered structure seen experimentally in the universe. It was even better that the fluctuations were small enough to suggest that the universe is finely balanced, so that it is either flat or slightly closed. This gives the first possible confirmation of the inflation hypothesis, which Guth invented to resolve the nonlinear problem of trying to extrapolate the present matter expansion back to the beginning at t = 0. One of the corollaries of this model is the requirement that the universe be almost flat.

Nevertheless, all attempts to simulate the growth of galaxies and galactic walls by numerical means have failed! One of the problems is that there isn't enough observed matter in the universe to make it flat, and another problem is that using mixtures of various postulated dark matter constituents to make up the difference doesn't produce galaxies with the right statistical distribution properties. In this regard, the experimental search to confirm the detection of any type of dark matter goes on in earnest, with no positive results so far. The next theoretical step, if all else fails, is to try to mine mass and energy from the false vacuum.

But I have argued here that dark matter must be discretely concentrated into planet or star-sized bodies in order to explain that the Solar System obeys Newton's Law. Hence, I don't expect that exotic dark matter particles will ever be detected.

If these dark matter experiments fail, will anyone finally admit that maybe a new model is needed that will provide an explanation in accordance with the wealth of otherwise unexplained experimental observations? I sincerely hope so!


Wave Models

  Conventional Analysis

A theoretical attempt has been made by Eisenstein et al to explain the spatial correlation in the NS galactic pencil surveys in terms of acoustic baryonic waves, consistent with the Cosmological Model. These results are essentially negative, in the sense that the only possibility of a solution with a flat universe requires too much baryonic matter to be compatible with the current model of Big Bang nucleosynthesis.

  New Big Wave Model

The Big Wave Model is based upon an analogy to the physics of neutron scattering by a nucleus. The incoming neutron is represented by a plane wave, which is decomposed into spherical Bessel function components to match the Center-of Mass system of the two particles. The Schrodinger Wave Equations are solved for the reflected spherical Bessel function components, which represent the scattered neutron. The probability of scattering the neutron is proportional to the square of the outgoing wave function. For some incident neutron energies, the wave contains a phase shift. The distances are small, and the neutron moves away from the nucleus at a non-relativistic velocity in a very short time.

The other analogy is the exponential attenuation of a beam of particles when it passes through matter. This solution occurs when the removal rate is directly proportional to the number of incident particles. There is also a geometrical attenuation of particles from a point source that is inversely proportional to the square of the distance from the point.

Both ideas are combined in the Big Wave Model. The incoming mass of black holes can be thought of as an incident spherically-symmetric jo Bessel wave function squared that preserves the energy and momentum of the black holes. After annihilation of the matter, we then consider an outgoing coherent jo Bessel wave function squared of photons and graviphotons, moving away from the origin at the speed of light, that has the same energy and momentum. The wavelength of this wave is of the order of 800 million light years, consistent with the properties of the graviton. It is accepted theoretically that essentially mass-less particles can possess very long wavelengths.

Since the wave packet moves away from the origin at the speed of light, only a small portion of the complete spherical traveling wave will be traced out at any given time and position. If we assume that the wave precipitates fast neutrons spatially at a rate proportional to the square of the wave function, then we have a matter deposition proportional to a periodic sine-squared function divided by the square of the distance from the origin. Geometric attenuation is included! If we further assume that the wave is attenuated exponentially as matter is precipitated, then we have additional damping.


Proof of the Pudding

The amazing thing is that the NS galactic pencil survey exhibits a damped sinusoidal behavior, with a highly correlated period of 428 million light years, out to a distance of about 5 billion light years in each direction from the Milky Way. The distribution is almost symmetric, as confirmed by a set of pairs correlations! When the pencil data are divided by the inverse square of the distance from the nodepoint at about 148 million light years south of the plane of the Milky Way, to remove the radial effects of cone-spreading, then the Big Bang Wave Model and the NS pencil data agree to a remarkable extent over the entire range of data.

Is this simply a case of curve fitting, or is there really something to this new Big Wave "theory" of creation? You decide!