I'm working on several projects but the one where I'm spending most time looks like this:
GR, in the PPN, fails to explain galaxy rotation curves. The gravitational potential going out from a spiral galactic center should be proportional to the inverse radius. Instead it's flat. The popular explanation for this invents dark matter. It's an ad hoc solution reminiscent of Ptolemy's epicycles, true until Copernicus found the heliocentric solution. In this case Moffat extended GR in an old way following somewhat the Brans Dicke model by introducing extra fields into the GR field equations. These extra fields go by names, Scaler, Vector, Tensor. When added to GR we have STVG whose fields have enough kick to flatten out the speed of stuff orbiting in a galaxy, and we keep the gravitic field in the mix in the geometrodynamic style formulation. The idea is to preserve GR but extend it in a way to accommodate certain subtleties we observe like flat galactic rotation curves without dark matter.
One thing Moffat doesn't address is the failure of the resulting STVG potential to be linear all the way out to the IGM. Instead, the potential falls below the PPN(quasi-Newtonian) value. Both STVG gravity and dark matter fail to explain this development.
I have an answer: a coupling of a combo of these fields to the field associated with a cosmological constant. When I manipulate Moffat's field equations I find the the scalar field drops out, and the remaining coupled vector tensor field equals the cosmological constant field with the Ricci tensor balanced by the mass-energy tensor of matter. What then drops out of the modified Moffat field equation, a component, is a radial differential equation well describing what has been measured in the rotation curves.
This model partially breaks geometrodynamics and implies that gravity is both geometry and a field in its own right. Nothing new about this, not even on this thread, because I've mentioned before here work by Babak and Grischuk, and Lugonov down the same lines. Currently, I'm trying to connect it all together. Probably I should communicate my results to Moffat, but I want to make sure everything makes sense. You have to be very careful when you trod on geometrodynamics, even a little. We'll see how it goes. |
