As space expands, the volume of the vacuum expands. That requires an increase in energy. The energy comes from the gravitational field that already exists. So, the strength of the field drops and the expansion accelerates. The expansion of the universe is driven by vacuum expansion. During the inflationary period, for the first nanosec of the universes existance, the vacuum energy was must higher due to the intial symmetry breaking at the beginning of time. Inflation ended and expansion began when the vacuum energy dropped.
Much of the dark matter is contained in particles called axions, which were found recently. The process that generates them, is what provides for CP symmetry in QCD/standard model.
"Vafa and Wesson that there are more temporal (time) dimensions – also that the extra dimension(s) can explain mass. (Particularly expanded dimensions versus compactified Kaluza-Klein dimensions.)"
Each of those particle models, with more than one time, has a corresponding string theory with compactified dimensions. The theories are the same, just different mathematical ways of looking at the same thing. Wesson's is a simple 10, or 11d string theory.
Randell's theories are on what's called anti-DeSitter Space, as opposed to DeSitter space. In DeSitter space, all the energy appears in the universe and the vacuum, and doesn't move back and forth. In anti-DeSitter Space it does. In string theory there are open strings and closed strings, which are loops. The end points of the open strings must lie on a brane. The universe consists of the strings and the branes. All interactions are string energies passing through the brane, between strings. If the ends of the string, weren't on a brane, the energy would arbitrarily wander off from the universe. Closed strings can't lose energy from the ends, because there is none.
In anti-DeSitter space(Randell) the grvitational coupling constant is high, the gravitons, which are closed strings, can lie off the branes and outside the universe. Some are essentially "in the vacuum". So, most of them do. The result is the few that remain in the regions around the brane, result in a weak field.
That Higgs boson experiment will be done next Nov. The guns haven't been as big as required so far, but CERN is. Regardless of the string theory and corresponding particle theory, such as Wessons, whatever is found will look just like a Higgs boson. That's because all the theories would show the same phenomina if they are correct. Differences are usually found in particle decays, like the proton decay rate, which causes some theories to fall.
I gave a decription of DeSitter space(dS) and AdS that left out one point. There are points on the energy scale that are Points of symmetry breaking. Coupling constants for the forces vary along that scale and merge at those points. ie the electromagnetic and weak force merge at one point, then merge with the strong force at higher energies. At those points, the symmetry breaking causes an increase in the vacuum energy. A reappearance of symmetry would cause a decrease.