Good question. I have asked myself the same thing, and I am afraid I can't answer it. I have some ongoing work on the matter, but so far its interesting mainly in the early universe. Though the anti-g matter becomes important again in the late stages of the expansion, it does not behave like a cosmlogical constant.
There are however several points in the whole scenario that I have not really thought through. If I had 5 postdocs, I would have no problem keeping them busy
Another interesting question about the Cosm. Const. is how the anti-g would affect the vacuum-energy in a quantized version. Make that 6 postdocs.