(Some people have commented in a way which indicates that they are here looking for a theory of gravity. This particular blog post is only tangentially related to gravity. This post exposes for the first time a little theory of Vector and scalar fields in curved space-time which could explain dark matter. NOT a theory of gravity per se. In fact for this work I am simply taking GR and a certain static curved background as a given.)
Let me explain. In standard and accepted quantum field theory in curved space time it is known that the local value of the metric will effect the probability of interactions occurring. However this geometric effect is usually so small compared ot the influence of the forces involved that it can be totally neglected. The value of the coupling constant, or charge, on the particles involved plays a much greater role. Never the less it is accepted theory that different observers following different path's through a curved space time will observe different numbers of particles. This is known as the Unruh effect.
What I realized was that the scalar and vector fields in theories of alternative gravity like Jacob Bekenstein's (Tensor Vector Scalar) TeVeS and John Moffat's (Scalar Tensor Vector Gravity) STVG are no different from any other fields. I did the calculations and sure enough they too are subject to differential interaction cross sections due to the geometric effect. This effect, which I detail in the linked PDF, is radially symmetric. The effect diverges at the origin, and has a sharp peak at a distance of one Schwarzchild radius from the center of a galaxy, then drops off as 1/r^4.
The difference between the dark forces and the forces we know and love could be the coupling constants. Which I cannot determine from theory alone. If their strength is comparable to or weaker than the geometric effect that would explain the lack of dark matter in the interior of the galaxy and why we have such trouble detecting any particles of dark matter. In our region of the galaxy due to the geometric effect the probability of interactions between dark matter particles is much greater than it is at cosmological distances from the galaxy. Higher probability of interaction means greater chances of an interaction destroying particles, as well as creating them. In this theory the Dark matter particles at cosmological distances from the galaxy are going to be more stable, and their distribution would be spherically symmetric about any galaxy or other collection of "ordinary matter". This could explain observations that suggest a spherical halo of dark matter surrounding spiral galaxy's.
This result shows that it is not necessary for alternative gravities to be at odds with observations of dark matter.
For the full theory please see.
Dark Matter and Energy as Particles and Fields of Unobserved Scalar and Vector
Fields (PDF) (rev2)..* **As submitted to a few Journals which I will not name.
(*It bears mentioning that just today I did a google search on vector scalar dark matter etc and found that work has been done in that direction. One piece I could find on Vector dark matter "Hidden vector dark matter." by )
**The reviewer at two of the journals say that a paper like this needs more experimental data to back it up. I don't know that there is much I can do about that. One said, interestingly that I should have used the Friedman Robertson Walker metric. This would not allow me to say anything about the dark matter in a specific galaxy, but it would tell me something about the universe as a whole. Perhaps it would tell me if this theory would lead to a distribution of dark matter which would prevent inflation. Or not. This is something I will look at in the coming weeks.
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