thank you for the link. Perhaps any conflict we had stems from my assumption that the model is seen in an absolute outside frame of reference, not from the viewpoint of an observer caught up on the membrane, or in the string. Or your attempts to project those effects into a negative pre-BB time frame.( a non existing situation in the model) Particularly the playing field, infinite time as a ur-paper surface, or as an ur-room, existing before our expanding space and it's starting point, puts it outside those theories. But inside spacetime, in the string or on the skin, I try to see these effects. I am looking for where it could be tweaked, I am sure, the stuck on the radius idea, because of maximum gravity is valid. so, I have no quarrel with Alber'ss results, just like to see how the Exp. Sph. model has to be modified, if necessary to accommodate.