Dark matter has proven harder to find than anyone anticipated in earth bound experiments, furthermore astronomical observations have revealed how it is spread through the universe.  How can these null results be explained? 

There are two kinds of searches for dark matter.  Those done in earth bound experiments, and those done with telescopes.  Astronomers have been very sure dark matter and dark energy exist for quite some time.  What they have been working on is figuring out its precise nature.  They consider dark matter composed of massive but non-radiating objects.  Particle physicists searching in earth bound experiments typically use devices cooled to liquid nitrogen or hydrogen temperatures to filter out temperature induced jitters in a search for massive elementary particles that do not interact with light or magnetism.   This last kind of dark matter, called Weakly Interacting Massive Particles (WIMPs) is the most accepted kind.  WIMPs make up the "Cold Dark Matter" in the standard model of cosmology, known as   (Lambda stands for dark energy and is the symbol for the cosmological constant in General Relativity.) 

On the particle physics side, there are experiments that have (and have not) claimed to detect , at least hints of dark matter.   The "detections" claimed so far are intriguing, but if one reads the fine print these are not certain detections at all.   By the standard methods of particle physics one has to be able to isolate their signal from the background noise out to five sigma, five standard deviations.  They need to be able to show a good sharp peak in their data.  No one in either camp described here, in detail, by Lubos Motl as the "good guys", who see dark matter, and "bad guys", who don't see dark matter, would claim such a clean signal. 

What the particle physics camp does have, is a recent result out of Italy which shows a signal just a bit stronger than the noise, but not by much.  For dark matter that's an achievement.

To put this in terms the average person is familiar with searching for particles is like searching the dial for distant radio stations.  When you are tuned in just right the signal is essentially static free and clear.  When you are not tuned in the signal is obscured by static and cross talk from other channels.    What has been found of dark matter so far is akin to a radio signal that you can sort of make out that it's not just static, but most of what you hear is static.  The kind of signal which seems to go away as soon as you take your hand off the dial (Okay, people much younger than me may have never tuned an analog radio or TV.  The digital equivalent I suppose could be having a YouTube video that plays like one word every so often but buffers most of the time.)

As for astronomical observations...

The most interesting observation I have seen in a while is that dark matter forms spherical halo's at characteristic distances from collections of normal luminous matter in "Universality of galactic surface densities within on dark halo scale-length", by Gentile et al (arXiv:0909.5203)  Across many galaxies it has been shown that the density of dark matter increases dramatically at a certain distance from the concentrated mass of the normal matter.  For every galaxy observed in their sample the inner boundary of the halo was at a point where the gravitational force had a certain constant value.   Why should this be the case?

I have a hypothesis which embraces both the unexpected difficulty in detecting dark matter, and the observation that it is concentrated at characteristic distances from galaxies.

In a nutshell, dark matter particles are associated with massive vector and scalar fields which decay as the strength of gravity increases.  The stronger the gravity the more rapid the decay.   In my paper, "A Lagrangian for the Lambda CDM Model" (Vixra:1106.0041)* I have spelled out this model in detail.   The action is as follows. 


What is old, or at least not new, are the basic forms of the fields in the Lagrangian.  They have all been published before in terms of theories of inflation, and alternative theories to General Relativity such as TeVeS.  What is different in this instance is I have treated them as functions of the Ricci curvature R.   Similar approaches have been taken in the program known as f(R) gravity.  In that case the Einstein-Hilbert action is generalized with functions of the Ricci Curvature. 

What is new and innovative is the following equation of constraint without which the theory does not predict a thing. 

In which the stress energy T is derived from the above action s.

Without belaboring details that are given in the formal paper what I do with these equations is use them to determine the masses of the scalar and vector fields.  These effective masses it will turn out depend on curvature.  The particles masses disappear, are zero,  when the curvature R attains a certain value.   A high value of the Ricci curvature R is associated with a strong gravitational field.    

The conversion of the mass of dark matter particles  into dark energy once the strength of gravity attains a certain critical value would explain the results discussed herein.  

If dark matter decays in the way described in my paper, and modeled with my math,  in the presence of strong gravity then of course it will be concentrated far far away from galaxies.  This same effect also explains why WIMPS have been even harder to detect than first expected.  Dark matter not only fails to interact via the electromagnetic and strong forces, it interacts with gravity in a fundamentally different way than ordinary matter. 

TL;DR: Dark matter has proven harder to find in Earth based experiments than previously thought, it has also been observed to form hollow halo's the inner surface of which lay at a characteristic distance from galaxies.  I present a hypothesis in which both problems are addressed by dark matter-energy fields which depend on Ricci curvature.   Strong gravity, means high curvature, and in this model these fields decay to almost nothing in the presence of strong gravity.  The result dark matter is going to be MUCH harder to find than anyone would like to think.

*The most recent version submitted to Physical Review Letters is not up on Vixra yet.  One errata in the version up as of my writing this blog entry is the constraint equation is confusingly listed along with the equations of motion.