In the following I will give some arguments that will indicate that the gravitational coupling "constant" actually depends on the scale (space and time) of the interacting systems. The question is:
Question 1. Which of the following arguments are invalid?
The following arguments are inspired by the following article:
"Loops, trees and the search for new physics", by Zvi Bern, Lance J. Dixon and David A. Kosower, Scientific American, Special Edition, "Extreme Physics".
The unitarity method (presented in this article and others), is a way of analysing particle processes that bypasses the complexity of Feynman's technique. Virtual particles are the prime reason why Feynman diagrams get so complicated. Virtual particles have both real and spurious effects, but the spurious effects cancel out of the final result (we can call this interference). The key to the success of the unitarity method is that it avoids the direct use of virtual particles. In this approach, it seems that each graviton behaves like two gluons stitched together.
Heisenberg's uncertainty principle will allow transitory fluctuations of energy that would allow processes involving multiple virtual particle loops to occur. These processes will have a very low probability of occurrence p. The average waiting time for such a process to occur will be around 1/p (the less likely the process is, the longer we have to wait, on the average, for it to occur). we also note that there are also many possible combinations, for a fixed number of gravitons and a fixed number of loops.
In QCD, it has been noticed that at very short distances (including distances relevant for collisions at LHC), the coupling diminishes in value, so theorists can get away with considering only uncomplicated diagrams.
A similar phenomenon (but at different relative scales) will appear in quantum gravity (when following the unitarity method, for example), when estimating the gravitational coupling constant (through actual measurement). The waiting time for the occurrence of processes associated with complex Feynman diagrams (that will affect the calculated value of the gravitational coupling constant) will be much longer than for the simple processes. Here I assume that in a theory of quantum gravity, the gravitational coupling constant can be estimated through measurement, and calculated based on the theory (as is the case for the electromagnetic coupling constant in QED).
Related to the dark matter problem, when scientists study the rotational speed of stars in a galaxy as a function of their distance from the galactic center, the system involves distances around thousands of light years (or more), and observation time of months or years. In this case, the gravitational coupling constant will have a greater value than in the case of systems at a lower scale. These scales leave plenty of room for the processes associated to complex Feynman diagrams to occur, thus affecting the value of the gravitational coupling constant (as compared to the Planck length 10^(-35) m, and Planck time 10^(-43) s). The force of gravity will seem stronger at larger scales.
The conclusion is that the gravitational coupling constant actually depends on the scale (in space and time) at which the act of measurement (observation) is performed. This does not exclude the possible existence of massive compact halo objects, WIMP particles, or other attempts to solve the dark matter problem, but I think that it plays a major role in this.
Question 2. Could this solve that dark matter problem?